Can the human mind learn to backward induce? A neural network answer.

This paper addresses the question of whether neural networks, a realistic cognitive model of the human information processing, can learn to backward induce in a two stage game with a unique subgame-perfect Nash Equilibrium. The result that the neural networks only learn a heuristic that approximates the desired output and does not backward induce is in accordance with the documented difficulty of humans to apply backward induction and their dependence on heuristics.behavioral game theory; neural networks; learning

Learning backward induction: a neural network agent approach

This paper addresses the question of whether neural networks (NNs), a realistic cognitive model of human information processing, can learn to backward induce in a two-stage game with a unique subgame-perfect Nash equilibrium. The NNs were found to predict the Nash equilibrium approximately 70% of the time in new games. Similarly to humans, the neural network agents are also found to suffer from subgame and truncation inconsistency, supporting the contention that they are appropriate models of general learning in humans. The agents were found to behave in a bounded rational manner as a result of the endogenous emergence of decision heuristics. In particular a very simple heuristic socialmax, that chooses the cell with the highest social payoff explains their behavior approximately 60% of the time, whereas the ownmax heuristic that simply chooses the cell with the maximum payoff for that agent fares worse explaining behavior roughly 38%, albeit still significantly better than chance. These two heuristics were found to be ecologically valid for the backward induction problem as they predicted the Nash equilibrium in 67% and 50% of the games respectively. Compared to various standard classification algorithms, the NNs were found to be only slightly more accurate than standard discriminant analyses. However, the latter do not model the dynamic learning process and have an ad hoc postulated functional form. In contrast, a NN agent’s behavior evolves with experience and is capable of taking on any functional form according to the universal approximation theorem.

The Evolution of Fairness under an Assortative Matching Rule in the Ultimatum Game

This paper studies how a matching rule affects the evolution of fairness in an ultimatum mini game. Gale et al. [1995] show that only selfish behaviour survives in the deterministic replicator dynamics under the random matching rule. In contrast, this paper shows that, under an assortative matching rule, the fair behaviour may survive at an asymptotically stable state.

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.

Investment Incentives in Auctions: An Experiment

We experimentally analyze first and second price auctions where one bidder can achieve a comparative advantage by investment prior to the auction. We find that, as predicted by theory, bidders invest more often prior to second price auctions than prior to first price auctions. In both auction formats bidding is more aggressive than the equilibrium prediction. However, bidding is closer to equilibrium than in control treatments where the comparative advantage is exogenous.Auctions, Investment Incentives, Asymmetric Auctions, Experimental Economics

Can Higher Bonuses Lead to Less Effort? Incentive Reversal in Teams

Conventional wisdom suggests that an increase in monetary incentives should induce agents to exert higher effort. In this paper, however, we demonstrate that this may not hold in team settings. In the context of sequential team production with positive externalities between agents, incentive reversal might occur: an increase in monetary incentives (either because rewards increase or effort costs decrease) may lead agents to exert lower effort in the completion of a joint task – even if agents are fully rational, self-centered money maximizers. Herein we discuss this seemingly paradoxical phenomenon and report on two experiments that provide supportive evidence.incentives, incentive reversal, team production, externalities, laboratory experiments, personnel economics

SOLOMON'S DILEMMA: AN EXPERIMENTAL STUDY ON DYNAMIC IMPLEMENTATION

This paper reports an experimental investigation on two mechanisms for the so-called King Solomon Dilemma, where one of them fails to implement the social choice rule dynamically. We compare the two mechanisms in terms of their welfare, incentive and learning properties.experiments, implementation, backward induction, bounded rationality

Drift effect and timing without observability: experimental evidence

We provide experimental evidence to Binmore and Samuelson’s (1999) insights for modeling the learning process through which equilibrium is selected. They proposed the concept of drift to describe the effect of perturbations on the dynamic process leading to equilibrium in evolutionary games with boundedly rational agents. We test within a random matched population two different versions of the Dalek game where the forward induction equilibrium weakly iterately dominates the other Nash equilibrium in pure strategies. We also assume that the first mover makes her decision first (“timing”) but the second mover is not informed of the first mover's choice (“lack of observability”). Both players are informed of their position in the sequence and of the fact that the second player will decide without knowing the decision of the first player. If the actual observed choices are only those made by other players in previous interactions, the role played by forward induction is replaced with the learning process taking place within the population. Our results support Binmore and Samuelson’s model because the frequency of the forward induction outcome is payoff-sensitive: it strongly increases when we impose a slight change in the payoffs that does not change equilibrium predictions. This evidence reinforces the evolutionary nature of the drift effect.evolutionary games, experiments, drift, forward induction, order of play. J.E.L. Classification: C72, C91

Experimental Evidence on the Multibidding Mechanism

Pérez-Castrillo and Wettstein (2002) and Veszteg (2004) propose the use of a multibidding mechanism for situations where agents have to choose a common project. Examples are decisions involving public goods (or public "bads"). We report experimental results to test the practical tractability and effectiveness of the multibidding mechanisms in environments where agents hold private information concerning their valuation of the projects. The mechanism performed quite well in the laboratory: it provided the ex post efficient outcome in roughly three quarters of the cases across the treatments; moreover, the largest part of the subject pool formed their bids according to the theoretical bidding behavior.experiments, mechanisms, uncertainty