Strategic behavior and counterfactuals (original) (raw)

Counterfactual Reasoning and Common Knowledge of Rationality in Normal Form Games

Topics in Theoretical Economics, 2004

When evaluating the rationality of a player in a game one has to examine counterfactuals such as "what would happen if the player were to do what he does not do?" In this paper I develop a model of a normal form game where counterfactuals of this sort are evaluated as in the philosophical literature (cf. Lewis, 1973; Stalnaker, 1968). According to this method one evaluates a statement like ``what would the player believe if he were to do what he does not do'' at the world that is closest to the actual world where the hypothetical deviation occurs. I show that in this model common knowledge of rationality need not lead to rationalizability. I also present assumptions that allow rationalizability to follow from common knowledge of rationality. These assumptions suggest that rationalizability may not rely on weaker assumptions about belief consistency than Nash equilibrium.

Non-additive beliefs and strategic equilibria

Games and Economic Behavior, 2000

This paper studies n-player games where players beliefs about their opponents behaviour are modelled as non-additive probabilities. The concept of an equilibrium under uncertainty which is introduced in this paper extends the equilibriumnotion of Dowand Werlang (1994) to n-player games in strategic form. Existence of such an equilibrium is demonstrated under usual conditions. For low degrees of ambiguity, equilibria under uncertainty approximate Nash equilibria. At the other extreme, with a low degree of confidence, maximin equilibria appear. Finally, robustness against a lack of confidence may be viewed as a refinement for Nash equilibria.

Beliefs correspondences and equilibria in ambiguous games

International Journal of Intelligent Systems, 2012

The Nash equilibrium concept combines two fundamental ideas. First, rational players choose the most preferred strategy given their beliefs about what other players will do. Second, it imposes the consistency condition that all players' beliefs are correct. This consistency condition has often been considered too strong, and different solution concepts have been introduced in the literature to take into account ambiguous beliefs. In this paper, we show, by means of examples, that in some situation beliefs might be dependent on the strategy profile and that this kind of contingent ambiguity affects equilibrium behavior differently with respect to the existing models of ambiguous games. Hence, we consider a multiple prior approach and subjective beliefs correspondences, which represent an exogenous ability of each player to put restrictions on beliefs over outcomes consistently with the strategy profile; we investigate existence of the equilibrium concepts corresponding to different attitudes toward ambiguity (namely, optimism and pessimism). Finally, we analyze particular beliefs correspondences: beliefs given by correlated equilibria and by ambiguity levels on events.

Equilibrium play and best response to (stated) beliefs in normal form games

Games and Economic Behavior, 2009

We report experimental results on one-shot two person 3x3 constant sum games played by non-economists without previous experience in the laboratory. Although strategically our games are very similar to previous experiments in which game theory predictions fail dramatically, 80% of actions taken in our experiment coincided with the prediction of the unique Nash equilibrium in pure strategies and 73% of actions were best responses to elicited beliefs. We argue how social preferences, presentation e¤ects and belief elicitation procedures may in ‡uence how subjects play in simple but non trivial games and explain the di¤erences we observe with respect to previous work.

Strategic interactions and belief formation: an experiment

Applied Economics Letters, 2010

Traditional models of belief formation in repeated games assume adaptive players who do not take strategic interactions into account. We find that these approaches are limited in the sense that people think more strategically and realize that, in contrast with the classical view, their own actions are likely to influence their opponents' behaviour.

Common belief of rationality in games of perfect information

Games and Economic Behavior, 2013

Aumann (1995) showed that for games with perfect information common knowledge of substantive rationality implies backward induction. Substantive rationality is defined in epistemic terms, that is, in terms of knowledge. We show that when substantive rationality is defined in doxastic terms, that is, in terms of belief, then common belief of substantive rationality implies backward induction. Aumann (1998) showed that material rationality implies backward induction in the centipede game. This result does not hold when rationality is defined doxastically. However, if beliefs are interpersonally consistent then common belief of material rationality in the centipede game implies common belief of backward induction.

Belief-Formation in Games of Initial Play : an Experimental Investigation

2019

Prior evidence suggests that individuals possess non-equilibrium beliefs in games of initial play. We investigate the belief-formation process in such settings with a lab experiment. Two main findings emerge from a novel elicitation task incentivizing participants to forecast the play of others. First, a subject anticipating a certain action generally predicts each and every less sophisticated action as well. Second, in the dynamic process of belief reporting, subjects order their predictions from less to more sophisticated strategies. The increasing use of non-equilibrium belief-based theories in strategic environments suggests that our results have implications in a variety of applications. ∗Fragiadakis: Villanova University, danielfragiadakis@gmail.com. Kovaliukaite: NYU Abu Dhabi, ada.kovaliukaite@gmail.com. Rojo Arjona: Chapman University, rojoarjo@chapman.edu. We are especially grateful to Alex Brown, Marco Castillo and Catherine Eckel for their impacts on the design and analy...

Ambiguous games with contingent beliefs

2010

The Nash equilibrium concept combines two fundamental ideas. First, rational players choose the most preferred strategy given their beliefs about what other players will do. Second, it imposes the consistency condition that all players' be-liefs are correct. This consistency condition ...