Chess players' performance beyond 64 squares: A case study on the limitations of cognitive abilities transfer

In a beauty contest experiment with over 6,000 chess players, ranked from amateur to world class, we found that Grandmasters act very similar to other humans. This even holds true when they play exclusively against players of approximately their own strength. In line with psychological research on chess players' thinking, we argue that they are not more rational in a game theoretic sense per se. Their skills are rather specific for their game.chess, beauty contest, cognitive transfer

Field Centipedes

We conduct a field experiment in which highly-ranked chess players play the centipede game in a natural setting. This game represents one of the main paradoxes of backward induction. In the experiment two players alternately are faced with the decision of either taking an exponentially growing pile of money and ending the game, or letting the other player make the decision. The player who decides to stop the game takes the larger portion of the pile, and the other player gets the remaining amount. All standard equilibrium concepts dictate that the player who decides first must stop the game immediately. There is vast experimental evidence, however, that this rarely occurs. Contrary to this evidence our results show that 69% of chess players stop the game immediately. When we restrict attention to chess Grandmasters this percentage escalates to 100%. We also conduct standard laboratory experiments where college students and chess players play ten repetitions of the game. We find that chess players playing versus other chess players rapidly converge to the equilibrium outcome, whereas students playing versus other students systematically depart from it. However, when students play against chess players the occurrence of the backward induction outcome increases tenfold.Rationality, centipede game, experiments, chess players.

Generalized backward induction: Justification for a folk algorithm

I introduce axiomatically infinite sequential games that extend Kuhn’s classical framework. Infinite games allow for (a) imperfect information, (b) an infinite horizon, and (c) infinite action sets. A generalized backward induction (GBI) procedure is defined for all such games over the roots of subgames. A strategy profile that survives backward pruning is called a backward induction solution (BIS). The main result of this paper finds that, similar to finite games of perfect information, the sets of BIS and subgame perfect equilibria (SPE) coincide for both pure strategies and for behavioral strategies that satisfy the conditions of finite support and finite crossing. Additionally, I discuss five examples of well-known games and political economy models that can be solved with GBI but not classic backward induction (BI). The contributions of this paper include (a) the axiomatization of a class of infinite games, (b) the extension of backward induction to infinite games, and (c) the proof that BIS and SPEs are identical for infinite games

Bargaining and Negotiations What should experimentalists explore more thoroughly?

A long time ago most economists would have limited themselves to stating that agreements should be individually rational and efficient and that selecting a specific agreement from that set depends on bargaining and negotiation power whatever that may be. Nowadays hardly any economist will argue that way. The change has been brought about by the strategic approach to bargaining and cooperation and the parallel experimental studies of bargaining and negotiation. When arguing what should be explored more thoroughly, we will point out directions where previous efforts may have been misdirected, where importing new methods may be helpful or even needed, and where new research questions need to be asked and answered.(un)bounded rationality, (non-)cooperative game theory, bargaining and negotiation (theory and experiments)

Counterfactual conditional analysis using the Centipede Game

The Backward Induction strategy for the Centipede Game leads us to a counterfactual reasoning paradox, The Centipede Game paradox. The counterfactual reasoning proving the backward induction strategy for the game appears to rely on the players in the game not choosing that very same backward induction strategy. The paradox is a general paradox that applies to backward induction reasoning in sequential, perfect information games. Therefore, the paradox is not only problematic for the Centipede Game, but it also affects counterfactual reasoning solutions in games similar to the Centipede Game. The Centipede Game is a prime illustration of this paradox in counterfactual reasoning. As a result, this paper will use a material versus subjunctive/counterfactual conditional analysis to provide a theoretical resolution to the Centipede Game, with the hope that a similar solution can be applied to other areas where this paradox may appear. The solution involves delineating between the epistemic systems of the players and the game theorists

A Game Theoretic Model for the Optimal Disposition of Integrated Air Defense System Assets

We examine the optimal allocation of Integrated Air Defense System (IADS) resources to protect a country\u27s assets, formulated as a Defender-Attacker-Defender three-stage sequential, perfect information, zero-sum game between two opponents. We formulate a trilevel nonlinear integer program for this Defender-Attacker-Defender model and seek a subgame perfect Nash equilibrium, for which neither the defender nor the attacker has an incentive to deviate from their respective strategies. Such a trilevel formulation is not solvable via conventional optimization software and an exhaustive enumeration of the game tree based on the discrete set of strategies is intractable for large problem sizes. As such, we test and evaluate variants of a tree pruning algorithm and a customized heuristic, which we benchmark against an exhaustive enumeration. Our tests demonstrate that the pruning strategy is not efficient enough to scale up to a larger problem. We then demonstrate the scalability of the heuristic to show that the model can be applied to a realistic size problem

Progress in Behavioral Game Theory

Is game theory meant to describe actual choices by people and institutions or not? It is remarkable how much game theory has been done while largely ignoring this question. The seminal book by von Neumann and Morgenstern, The Theory of Games and Economic Behavior, was clearly about how rational players would play against others they knew were rational. In more recent work, game theorists are not always explicit about what they aim to describe or advise. At one extreme, highly mathematical analyses have proposed rationality requirements that people and firms are probably not smart enough to satisfy in everyday decisions. At the other extreme, adaptive and evolutionary approaches use very simple models-mostly developed to describe nonhuman animals-in which players may not realize they are playing a game at all. When game theory does aim to describe behavior, it often proceeds with a disturbingly low ratio of careful observation to theorizing

Sequential Two-Player Games with Ambiguity

If players' beliefs are strictly non-additive, the Dempster-Shafer updating rule can be used to define beliefs off the equilibrium path. We define an equilibrium concept in sequential two-person games where players update their beliefs with the Dempster-Shafer updating rule. We show that in the limit as uncertainty tends to zero, our equilibrium approximates Bayesian Nash equilibrium by imposing context-dependent constraints on beliefs under uncertainty.