Endogenous definition is - growing or produced by growth from deep tissue. How to use endogenous in a sentence. Did You Know?. Endogenous substances and processes are those that originate from within an organism, tissue, or cell. Endogenous viral elements are DNA sequences derived . Endogenous definition, proceeding from within; derived internally. See more.
Details of the test are contained in the Online Appendix. The objective of treatment [C] is to test the theoretical predictions on higher-order beliefs effects. The precise wording of treatment [C] is designed to pin down the entire hierarchy of beliefs, as described in Section For instance, the full description that a math and sciences student is given concerning his opponent in treatment [C] is: You play against the number that one of them has picked. As argued by Arad and Rubinstein , the 11—20 game presents a number of advantages in the study of sequential reasoning, which are inherited by our modified version.
We recall here the most relevant to our purposes. First, using sequential reasoning is natural, as there are no other obvious focal ways of approaching the game. Note that our aim is not to establish the type of reasoning process itself, which we take as given, and has been an important contribution of the literature see, in particular, the seminal papers by Nagel, ; Camerer et al.
Moreover, it is the unique best choice for a player who ignores all strategic considerations. Thirdly, there is robustness to the anchor specification, in that the choice of 19 would be the best response for a wide range of anchors, including the uniform distribution over the possible actions. Lastly, best-responding to any action is simple. Since we do not aim to capture cognitive limitations due to computational complexity, having a simple set of best responses is preferable.
In addition to these points, our modification of the 11—20 game breaks the cycle in the chain of best responses, which is crucial for our testable predictions. We present, for brevity, only the experimental results for the grouped exogenous and endogenous classifications. Moreover, we present the results by pooling together the treatments when they are repeated.
For these repetitions, our pooling is justified by tests for equality of distribution. We analyse first the results when subjects' payoffs are changed, followed by the results when their beliefs over opponents are varied. We discuss in this section the Wilcoxon signed-rank tests and the regressions, and defer further details to Appendix B.
In the random-effects ordinary least squares OLS estimations that follow, we regress, for each label, the outcome on a dummy for the treatments, and another for the classification endogenous or exogenous. The latter is never significant. All regressions and statistical tests are in Appendix B. The OLS regressions are in Table 5 of Appendix B and the Wilcoxon signed-rank tests for changes in payoffs and beliefs over opponents are in Tables 6 and 7 , respectively.
As the value of reasoning increases for players and their opponents, the model predicts that they would choose actions associated with higher k 's. These implications hold for both label I and label I I subjects. Changing payoffs, label I left and label I I right. Recall that label I denotes the high score and math and sciences combined, and label I I the low scores and humanities combined. For both labels, increasing incentives shifts the level of play towards more sophisticated behaviour i.
This holds within each treatment: These results are therefore consistent with our theoretical predictions. These findings are consistent with the theory, and with the view that agents perform more rounds of reasoning if the incentives are increased. These results also indicate that changing from an extra 20 tokens to an extra 80 tokens determines a large enough shift in the value function that it leads agents to increase their level of reasoning.
The graphs in Figure 4 depict the shifts in the distributions. Consider the comparison between homogeneous treatment [A], heterogeneous treatment [B], and replacement treatment [C]. These predictions are consistent with the data displayed in Figure 5. Distribution [C] clearly stochastically dominates [B] everywhere, and [B] stochastically dominates [A] nearly everywhere. Changing beliefs comparison of treatments [A] and [B] affects behaviour in a way consistent with our model.
Moreover, as predicted by our theory, higher-order beliefs effects comparison of treatments [B] and [C] are observed only for the more sophisticated subjects label I.
The estimates comparing [B] to [C], however, are not significant. Figure 5 reveals that distributions [B] and [C] remain very close to each other, and so the lack of significance is not surprising. Here, no clear difference emerges from Figure 5 between the three cumulative distributions. Conducting Wilcoxon signed-rank equality of distribution tests confirms the visual intuition, and the OLS estimates are not significant for any of the comparisons of [A] to [B], [B] to [C], or [A] to [C].
Additional observations are discussed in the Online Appendix. In summary, the experimental results are consistent with our model's predictions. More broadly, our findings also show that individuals change their actions as their incentives and beliefs about the opponents are varied, and that they do so in a systematic way.
This illustrates the empirical need for a model that endogenizes depth of reasoning, and supports our approach. In this section, we show that our model can be applied to make predictions across games, thereby shedding light on open empirical questions. In particular, we show that the predictions of our model are highly consistent with Goeree and Holt's , henceforth GH well-known findings.
In this influential paper, GH conduct a series of experiments on initial responses in different games. GH show that classical equilibrium predictions often perform well in the treasure, but not in the contradiction. As they, and others since, note, it is important to have a model that explains these intuitive patterns of behaviour. But these results have been difficult to explain both qualitatively and quantitatively, particularly without making ad hoc assumptions for each game. Our model provides a unified explanation for GH's observed results.
We argue that this explanation has qualitative appeal and show that it is highly predictive of GH's data. In this analysis, we consider a version of the model with a single free parameter and calibrate that parameter using one of GH's games. We then use this parameter, holding it fixed throughout, to predict behaviour in GH's other static games of complete information the domain of our theory. We do not exploit any other degree of freedom, thereby further ensuring that our analysis does not make use of ad hoc assumptions.
Comparing our predictions to the data reveals that our results are indeed strongly in line with GH's findings. Here we illustrate the logic behind the results, leaving the details of the quantitative analysis to Appendix C. We first review GH's findings and briefly discuss why a classical level- k approach does not suffice to explain them. We then present the results of our calibration. Nash equilibrium predicts that both the row and the column players mix uniformly over their two actions.
Since x does not affect the payoffs of the column player, in any Nash equilibrium the distribution over the row player's actions should be uniform independent of x. The following game, also parameterized by x , is a coordination game with one efficient and one inefficient equilibrium, which pay , and 90 , 90 , respectively. The column player also has a secure option S which pays 40 independent of the row player's choice.
Notice that action S is dominated by a uniform distribution over L and H. Hence, changing x has no effect on the set of equilibria. However, GH's experimental data show that behaviour is strongly affected by x. In this version of Basu's well-known game, two players choose a number between and inclusive.
The reward they receive is equal to the lowest of their reports, but in addition the player who announces the higher number transfers a quantity x to the other player. Players in this game choose effort levels a 1 and a 2 which can be any integer between and Independent of x , any common effort level is a Nash equilibrium. The efficient equilibrium is the one with high effort. While the pure-strategy Nash equilibria are unaffected by this change in payoffs, GH's experimental data show that agents exert lower effort when x is higher.
The modified game is obtained from the baseline simply by adding a constant of to every payoff, which does not affect the equilibria. This game has two pure-strategy equilibria, T o p , L e f t and B o t t o m , R i g h t , and one mixed-strategy equilibrium in which row randomizes between T o p and B o t t o m and column randomizes between L e f t and M i d d l e. Yet, a majority of column players choose the Non-Nash action. In this case as well, the change in payoffs has no effect on the column players, and only a small one on the row players.
The results of these experiments stand in sharp contrast with standard equilibrium concepts. Concerning the classical level- k approach, while it has convincingly demonstrated that individuals follow sequential reasoning processes, we have shown in the previous sections that it is important to endogenize the depth of reasoning when making predictions across games, particularly when incentives to reason vary, as in GH's setting.
The changes in incentives can impact individuals' cognitive bounds and beliefs, and hence, the level according to which they play. This suggests that conducting a level- k analysis without accounting for these factors in GH's setting could be incomplete, which seems to be the case empirically. For instance, as GH point out, the results of the Traveller's Dilemma would require an unusual distribution of levels GH, p.
Clearly, imposing the same parameters as for Matching Pennies worsens the fit. The analysis that follows demonstrates the importance of accounting for variations in the depth of reasoning. The logic that drives the results is intuitive, further illustrating that this model is well-suited to explain GH's findings.
A common feature of the GH's treasures and contradictions is that the observed behaviour appears intuitive and fundamentally linked to the nature of incentives. In all five games, the treasure and contradictions differ in a payoff parameter x which does not affect the pure actions best-reply functions. In the language of Section 2 , this means that each treasure and its contradictions belong to the same cognitive equivalence class. Hence, we can use our model to understand the change of behaviour by studying how varying the parameter x affects players' incentives to reason, holding the costs of reasoning constant.
To demonstrate that our analysis does not provide us with too much flexibility, we allow only one degree of freedom in the model. We then calibrate the single free parameter using one of GH's games, and hold its value constant not only between a treasure and its contradictions, but throughout the games. Our predictions fit the empirical findings closely even with these stringent restrictions, thereby providing strong support for our theory.
We choose this functional form because it illustrates cleanly the logic of the model, and because it restricts the degrees of freedom available by completely fixing the value of reasoning. Other plausible representations, such as equation 4 in Example 2 , would allow for more degrees of freedom and would improve our estimates. Similarly, allowing for more types of sophistication would also clearly improve the fit of our predictions to the data, without adding to the basic intuition.
We use the Matching Pennies game described above to describe the way our model applies to GH's games. Following the reasoning from Section 2. We thus start by characterizing the cognitive bound of the low types, and hence their chosen action, before discussing the high types. For a row player whose current action is B , sufficiently increasing x will lead him to perform one extra step of reasoning, and eventually stop at T.
For a row player whose current level is T , the increase in x has no effect. Hence, for a sufficiently high increase in x , any low type player 1 will stop his reasoning at T. This does not depend on the anchor a 0. Hence, as x increases, either the low type player 1's behaviour stays the same, or for sufficiently high x he plays T , independent of the anchor. Consider now the low type of player 2, who also plays according to his cognitive bound.
Because x has no impact on his value of reasoning, his behaviour does not change. Turning to the high types, their behaviour depends not only on their cognitive bound, but also on their beliefs over the low types' behaviour.
A high-type player 1 plays T if he believes a high fraction plays L , and a high-type player 2 chooses R if he believes a high enough fraction plays T. In essence, not only does the increase in x have an impact on the cognitive bound of player 1s, but it also has an effect on the high types' beliefs over their opponents' cognitive bound.
This in turn affects their behaviour in a predictable way: To summarize, actions chosen for the low-type players depend only on their own cognitive bound, while those of the high-type players also depend on their beliefs over the low types' play. Moreover, as payoffs are made asymmetric through the increase in x , incentives to reason are distorted.
For high enough asymmetries, the anchor itself is no longer relevant: Depending on the parameter q l , this in turn pins down the behaviour of the high types. Our calibration exercise is based on this logic, and uses the data from one game to identify q l.
We then use the calibrated parameter to predict the choices for the remaining games. We emphasize that the value of reasoning function is fully determined, and the only property of the cost functions used in this argument is that they are increasing. No further assumptions on the cost functions are needed.
Regressions for labels I and I I. Standard errors in parentheses. The data for the last three games Kreps', Minimum-Effort Coordination and the Traveller's Dilemma are fully consistent with the restrictions and calibrated parameter discussed above, but they do not require the full force of our assumptions. For the Kreps game, for instance, the implications of our model are the simplest of all: Hence, the model predicts that whatever we observe in the baseline game should not change for the modified game.
This prediction is close to the observed behaviour, especially for the column players. These results are close to the empirical findings, which are mainly concentrated near and , respectively. In the Traveller's Dilemma, as x increases, Assumption 4 implies that the value of reasoning increases. Hence, by Proposition 2, individuals' depth of reasoning would be higher in the high-reward treatment, and their chosen action would be lower.
The assumptions specified above, and the calibrated parameter for q l , are entirely consistent with this result, but they are not necessary for this analysis. These parameters can serve, however, to enable a partial identification of the shape of the cost function.
Identifying the cost of reasoning in different strategic settings is an important empirical question for future research. In this article, we have introduced a model of strategic thinking that endogenizes individuals' cognitive bounds as the result of a cost—benefit analysis. Our theory distinguishes between players' cognitive bounds and their beliefs about the opponent's bound, and accounts for the interactions between depth of reasoning, incentives, and higher-order beliefs.
The tractability of the model has guided our experimental design to test these complex interactions. From a theoretical viewpoint, we extend the general level- k approach of taking reasoning in games to be procedural and possibly constrained. By making explicit these appealing features of level- k models, our framework serves to attain a deeper understanding of the underlying mechanisms of that approach. Our framework also solves apparent conceptual difficulties of the level- k approach, such as the possibility that individuals reason about opponents they regard as more sophisticated.
In addition to testing the model, our experiment plays a broader role. It reveals that individuals change their behaviour in a systematic way as their incentives and beliefs are varied. Thus, caution should be exercised in interpreting level of play as purely revealing of cognitive ability, as an endogeneity problem is present.
This provides further support for our theory and an external validation of the approach. Since Goeree and Holt's games have a very different structure from those of our experiment, this exercise also shows that our theory is applicable to a wide range of games.
In closing, we note that our theory establishes a link between level- k reasoning and the conventional domain of economics, centred around tradeoffs and incentives. From a methodological viewpoint, this can further favour the integration of theories of initial responses within the core of economics. Conversely, the application of classical economic concepts to a model of reasoning opens new directions of research both theoretically and empirically.
For instance, future research could include a rigorous identification of the properties of cost functions in different games and testing predictions of changes in behaviour across other strategic settings. No subject took part in more than one session. Subjects were paid 3 euros for showing up students coming from a campus that was farther away received 4 euros instead.
Subjects' earnings ranged from 10—40 euros, with an average of Each subject went through a sequence of 18 games. Subjects were paid randomly, once every six iterations.
The order of treatments is randomized see below. Finally, subjects only observed their own overall earnings at the end, and received no information concerning their opponents' results. Our subjects were divided in six sessions of twenty subjects, for a total of subjects.
Three sessions were based on the exogenous classification, and each contained ten students from the field of humanities humanities, human resources, and translation , and 10 from math and sciences math, computer science, electrical engineering, biology, and economics. Three sessions were based on the endogenous classification, and students were labelled based on their performance on a test of our design. See the Online Appendix. We describe next the instructions as worded for a student from math and sciences.
The instructions for students from humanities would be obtained replacing these labels everywhere. Similarly, labels high and low would be used for the endogenous classification. Pick a number between 11 and You will always receive the amount that you announce, in tokens. In other words, two students from humanities play against each other. You are now playing a high-payoff game. In other words, two students from humanities play the high-payoff game with each other extra 10 if they tie, 80 if exactly one less than opponent.
Our six groups three for the endogenous and three for the exogenous classification went through four different sequences of treatments. Two of the groups in the exogenous treatment followed Sequence 1, and one followed Sequence 2. The three groups of the endogenous classification each took a different sequence: The order of the main treatments is different in each sequence, both in terms of changing the beliefs and the payoffs.
These sequences include additional treatments [K], [L], [D], [E], and [F] discussed in the working paper. The paths of reasoning have a periodicity of 4. The cases for the other three possible anchors are obtained similarly. Let v 80 denote such a function. Now, suppose that x is increased above 80, and consider the low types of population 1. For these players, the value of reasoning is no longer constant: Their depth of reasoning, therefore, does not change either.
Above that threshold, all the low types of population 1 play T , the behaviour of low types in population 2 remains the same, and behaviour of the high types depends on q l. It follows that all types will play at their cognitive bound. In particular, this implies that the actions of both types in population 2 are uniformly distributed. The low types of population 2 instead are uniformly distributed, following their own cognitive bound. The remaining half of high types of population 1 believe the low types of population 2 play R , hence they play B.
Given c l , depending on what the anchor is, we may have the following cases: In this case, which applies to half of the population, the low types of population 2 play L. The low types of population 1 play T , because their increased incentives moved their cognitive bound to T. They thus play at their bound. In this case, which applies to a quarter of the population, the low types of population 2 play R and the low types of population 1 play T.
Since the high types in population 2 have the same cost function, but higher incentives, they would be able to anticipate this, and respond playing L. The predictions of the model, therefore, are the following:. Oxford University Press is a department of the University of Oxford. It furthers the University's objective of excellence in research, scholarship, and education by publishing worldwide.
Sign In or Create an Account. D80 - General All Journals search input. Close mobile search navigation Article navigation. Endogenous Depth of Reasoning Larbi Alaoui. Department of Economics, University of Wisconsin-Madison. Abstract We introduce a model of strategic thinking in games of initial response. We introduce next a mapping to identify the intersection between the value of reasoning and the cost function: Given cost and value functions c i , v i , the cognitive bound of player i is defined as: View large Download slide.
To extend the logic above to non-degenerate beliefs, it suffices to adjust the recursion by requiring that types best respond to the induced distribution of the opponents' actions.
Formally, fix a general CTS. The recursion becomes constant for a type at iterations above its cognitive bound. This represents the idea that the type's reasoning has stopped. Recursively, the iteration also becomes constant for types that place sufficiently high probability on types whose own recursion has become constant.
As for the case with degenerate beliefs, this could be either because they have reached their bound, or recursively because they believe the opponent has, and so forth. Thus, a type's optimal behaviour given his beliefs and cognitive bound can be obtained once the corresponding recursion has become constant, which happens no later than at the iteration corresponding to that type's cognitive bound and exactly at that step, if the bound is indeed binding.
Changing payoffs, label I left and label I I right Notes: The baseline and the modified games are described in the following table. The numbers in parentheses represent the empirical distributions observed in the experiment: We maintain the following assumptions: Let q l denote the fraction of the low types.
Fraction q l is the parameter that we calibrate using one game and maintain as constant throughout all games and for both players. For identification purposes, we also assume that agents have correct beliefs over the distribution of types.
Given the functional form in equation 11 , the value of reasoning is: This game has two pure-strategy Nash equilibria, L , L and H , H , which are not affected by the value of x. Nonetheless, it shapes player 1's incentives to reason, as an increase in x changes the value of doing a step of reasoning when player 1 is in a state in which action H is regarded as the most sophisticated. Applying equation 11 to this game, with payoffs parameterized by x , we obtain the following value of reasoning functions: For the same reasons discussed above, for any pair of increasing cost functions c l , c h , there exists an x sufficiently high that all low types of population 1 with a reasoning process that involves a cycle stop at L.
Since the incentives to reason were not affected by the change in x for these individuals, the assumptions above imply that they play H. It remains to consider the high types of population 1. The others play L. To determine the percentages of coordination in L , L and H , H , we assume independence in the distributions of play between the row and the column players. The Money Request Game: A Level- k Reasoning Study. One, Two, Three , Infinity…: Newspaper and Lab Beauty-Contest Experiments.
Lying for Strategic Advantage: Rational and Boundedly Rational Misrepresentation of Intentions. Structural Models of Nonequilibrium Strategic Thinking: Theory, Evidence, and Applications. Who Knows It Is a Game? Cognitive Ability and Learning to Play Equilibrium: A Level- k Analysis. A Level- k analysis. For a recent survey on the empirical and theoretical literature on strategic thinking see Crawford et al. Particularly important within this area is the literature on level- k reasoning, first introduced by Nagel and Stahl and Wilson , Level- k models have been extended to study communication Crawford, , incomplete information Crawford and Iriberri, and other games.
For recent theoretical work inspired by these ideas, see Kets , Kneeland and Strzalecki's The as-if approach, in which the cost—benefit analysis need not be viewed as being performed consciously, circumvents the infinite regress problem in which it would be costly to think about how to determine the value of reasoning, which itself is costly, and so forth see Lipman, In Alaoui and Penta we pursue an axiomatic approach to players' reasoning, in which the cost—benefit analysis emerges as a representation.
Recent work by Choi also incorporates a cost—benefit approach in a setting of strategic thinking and learning in networks. We discuss the connections with that paper and other related models in Section 2. A recent experiment by Agranov et al. Palacios-Huerta and Volij explore a related point in the dynamic context of the centipede game. This is also the game used in the experiment of Section 3. We defer to that section the discussion of the properties of this game, and its suitability to our objectives.
If a j k is a mixed action, i 's best response need not be unique. In that case, we assume that the action is drawn from a uniform distribution over the best responses. As we will discuss in Section 3 , different specifications of the level-0 including the uniform distribution would not affect the analysis. Formalizing this notion is often perceived to be a fundamental difficulty in developing a theory of bounded rationality; in this model it emerges naturally.
Note that j does not observe the rounds of reasoning as i performs them, and so additional reasoning cannot have negative value from becoming common knowledge. In initial response settings, the value of reasoning need not coincide with the actual gain in payoffs.
It may appear plausible that the player stops reasoning if he believes that his opponent has already reached his bound, because the extra steps of reasoning would not affect the player's own choice. This alternative formulation can be easily accommodated in our model, which accounts for beliefs, through a reinterpretation of some of the variables.
In this example, the change in payoffs plays no role in the player's decision. This approach, also known as the interim approach , is the standard one to study non-equilibrium concepts with incomplete information see, e. Weinstein and Yildiz, , ; or Penta, , It is easy to verify that the simplified model of the previous section obtains as the special case of second-order types with degenerate beliefs: See, for instance, Stahl and Wilson , , Costa-Gomes et al.
For an experimental study of equilibrium in a related game, see Capra et al. Our theoretical predictions on the shift of the distribution do not depend on assumptions of degenerate beliefs; as discussed in Section 2 , our model allows for non-degenerate beliefs. Noise in the path of reasoning, in the spirit of Goeree and Holt , can be introduced as well. These views emerged from informal conversations with students. They are confirmed by the admission scores, used to select the students admitted in the various fields.
These scores can be found at: For studies that focus more directly on the cognitive process itself, see Agranov et al. See also Georganas et al. The figures for the separate classifications are consistent with the results for the grouped classifications. The only exception is at action 19, which is consistent with the well-known observation that stochastic dominance relations are often violated near the endpoints, even when the true distributions are ranked.
GH do not specify the rule in case of tie. We assume that there are no transfers in that case. We maintain that anchors are uniform to avoid ad hoc assumptions. We do not make cognitive equivalence assumptions other than for each treasure and its respective contradictions.
For instance, the costs of reasoning for Matching Pennies and its contradictions need not be the same as in the Traveller's Dilemma and its contradiction. In the other games, the increase in x has an identical effect for player 1 and player 2. These data however are inconsistent, probably due to a typographical error: In a different setting, it is a well-known theme in the Economics of Education literature that incentives may affect standard measures of cognitive abilities.
For a recent survey of the vast literature that combines classical economic notions with measurement of cognitive abilities and psychological traits to address the endogeneity problems stemming from the role of incentives, see Almlund et al. While we think this is a plausible explanation, we explore here to what extent the mere change in incentives may explain the observed variation in behaviour, independent of the possible change in the anchors. We note that assuming that the anchor is the uniform distribution delivers very similar quantitative results.
Words that rhyme with endogenous. Translation of endogenous for Arabic Speakers. What made you want to look up endogenous? Please tell us where you read or heard it including the quote, if possible. Test Your Knowledge - and learn some interesting things along the way. Subscribe to America's largest dictionary and get thousands more definitions and advanced search—ad free! You'll fall head over heels. Is it real life, or just fantasy?
Comedian ISMO on what separates a boot from a trunk. Comedian ISMO on the complexities of the word 'tip'. How to use a word that literally drives some people nuts. The awkward case of 'his or her'. Test your vocabulary with our question quiz! Facebook Twitter YouTube Instagram. Other Words from endogenous Did You Know? More Example Sentences Learn More about endogenous. Other Words from endogenous endogenously adverb. Examples of endogenous in a Sentence Recent Examples on the Web Second, the neutral rate is endogenous to economic policy.
Definition of endogenous - having an internal cause or origin. endogenous (comparative more endogenous, superlative most endogenous). Produced, originating or growing from within. Of a natural process, or caused by. endogenous definition: 1. found or coming from within something, for example a system or a person's body or mind: 2. used in economics to describe something.