Learning to be unpredictable : an experimental study.

This study tests experimentally whether the ability of subjects to play a noncooperative game's mixed-strategy equilibrium (to make their play unpredictable) is affected by how much information subjects have about the structure of the game. Subjects played the mixed-strategy equilibrium when they had all the information about other players' payoffs and actions, but not otherwise. Previous research has shown that players of a game can play a mixed-strategy equilibrium if they observe the actions of all players and use sophisticated Bayesian learning to infer the likely payoffs to other players. The result of this study suggests that the subjects in our experiments did not use sophisticated Bayesian learning. The result also suggests that economists should be careful about assuming in their models that people can easily infer everyone else's payoffs.Game theory

Knowledge Spaces and the Completeness of Learning Strategies

We propose a theory of learning aimed to formalize some ideas underlying Coquand's game semantics and Krivine's realizability of classical logic. We introduce a notion of knowledge state together with a new topology, capturing finite positive and negative information that guides a learning strategy. We use a leading example to illustrate how non-constructive proofs lead to continuous and effective learning strategies over knowledge spaces, and prove that our learning semantics is sound and complete w.r.t. classical truth, as it is the case for Coquand's and Krivine's approaches

Learning, Information and Sorting in Market Entry Games: Theory and Evidence

Previous data from experiments on market entry games, N-player games where each player faces a choice between entering a market and staying out, appear inconsistent with either mixed or pure Nash equilibria. Here we show that, in this class of game, learning theory predicts sorting, that is, in the long run, agents play a pure strategy equilibrium with some agents permanently in the market, and some permanently out. We conduct experiments with a larger number of repetitions than in previous work in order to test this prediction. We find that when subjects are given minimal information, only after close to 100 periods do subjects begin to approach equilibrium. In contrast, with full information, subjects learn to play a pure strategy equilibrium relatively quickly. However, the information which permits rapid convergence, revelation of the individual play of all opponents, is not predicted to have any effect by existing models of learning.

Knowledge Spaces and the Completeness of Learning Strategies

We propose a theory of learning aimed to formalize some ideas underlying Coquand\u27s game semantics and Krivine\u27s realizability of classical logic. We introduce a notion of knowledge state together with a new topology, capturing finite positive and negative information that guides a learning strategy. We use a leading example to illustrate how non-constructive proofs lead to continuous and effective learning strategies over knowledge spaces, and prove that our learning semantics is sound and complete w.r.t. classical truth, as it is the case for Coquand\u27s and Krivine\u27s approaches

Incentive and stability in the Rock-Paper-Scissors game: an experimental investigation

In a two-person Rock-Paper-Scissors (RPS) game, if we set a loss worth nothing and a tie worth 1, and the payoff of winning (the incentive a) as a variable, this game is called as generalized RPS game. The generalized RPS game is a representative mathematical model to illustrate the game dynamics, appearing widely in textbook. However, how actual motions in these games depend on the incentive has never been reported quantitatively. Using the data from 7 games with different incentives, including 84 groups of 6 subjects playing the game in 300-round, with random-pair tournaments and local information recorded, we find that, both on social and individual level, the actual motions are changing continuously with the incentive. More expressively, some representative findings are, (1) in social collective strategy transit views, the forward transition vector field is more and more centripetal as the stability of the system increasing; (2) In the individual behavior of strategy transit view, there exists a phase transformation as the stability of the systems increasing, and the phase transformation point being near the standard RPS; (3) Conditional response behaviors are structurally changing accompanied by the controlled incentive. As a whole, the best response behavior increases and the win-stay lose-shift (WSLS) behavior declines with the incentive. Further, the outcome of win, tie, and lose influence the best response behavior and WSLS behavior. Both as the best response behavior, the win-stay behavior declines with the incentive while the lose-left-shift behavior increase with the incentive. And both as the WSLS behavior, the lose-left-shift behavior increase with the incentive, but the lose-right-shift behaviors declines with the incentive. We hope to learn which one in tens of learning models can interpret the empirical observation above.Comment: 19 pages, 14 figures, Keywords: experimental economics, conditional response, best response, win-stay-lose-shift, evolutionary game theory, behavior economic