Dynamics of Internal Models in Game Players

A new approach for the study of social games and communications is proposed. Games are simulated between cognitive players who build the opponent's internal model and decide their next strategy from predictions based on the model. In this paper, internal models are constructed by the recurrent neural network (RNN), and the iterated prisoner's dilemma game is performed. The RNN allows us to express the internal model in a geometrical shape. The complicated transients of actions are observed before the stable mutually defecting equilibrium is reached. During the transients, the model shape also becomes complicated and often experiences chaotic changes. These new chaotic dynamics of internal models reflect the dynamical and high-dimensional rugged landscape of the internal model space.Comment: 19 pages, 6 figure

Players with Limited Memory

This paper studies a model of memory. The model takes into account that memory capacity is limited and imperfect. We study how agents with such memory limitations, who have very little information about their choice environment, play games. In particular, the players do not know if they are playing a game. We show that players do better in games than in decision problems. This is because the players, unknowingly, improve the environment they face in games. We also show that people can do quite well in games even with severely limited memories, although memory restrictions tend to make them behave cautiously. Lastly, we introduce a solution concept approiate for analysis games in which the players may have limited knowledge of their environment and have some memory restictions. We show hos this solution concept is related to other like the iterated removal of strictly dominated strategies.

Learning to Respond: The Use of Heuristics in Dynamic Games

While many learning models have been proposed in the game theoretic literature to track individuals’ behavior, surprisingly little research has focused on how well these models describe human adaptation in changing dynamic environments. Analysis of human behavior demonstrates that people are often remarkably responsive to changes in their environment, on time scales ranging from millennia (evolution) to milliseconds (reflex). The goal of this paper is to evaluate several prominent learning models in light of a laboratory experiment on responsiveness in a lowinformation dynamic game subject to changes in its underlying structure. While history-dependent reinforcement learning models track convergence of play well in repeated games, it is shown that they are ill suited to these environments, in which sastisficing models accurately predict behavior. A further objective is to determine which heuristics, or “rules of thumb,” when incorporated into learning models, are responsible for accurately capturing responsiveness. Reference points and a particular type of experimentation are found to be important in both describing and predicting play.learning, limited information, dynamic games

Anscombe on the mesmeric force of ‘ought’ and a spurious kind of moral realism

I discuss the second of the three theses advanced by Anscombe in ‘Modern Moral Philosophy’. The focus is the nature of entities to which – if Anscombe’s diagnosis is correct – ought and cognate modals are assumed by modern moral philosophers to refer. I reconstruct the alternative account offered by Anscombe of viable and justified ‘Aristotelian’ modals – as contrasted with mysterious and unjustified ‘Kantian’ modals; I discuss the nature and status of ‘Aristotelian necessity’ to which such legitimate modals refer to. I conclude with the claims that Anscombe’s account of modern moral philosophy is viciously parochial, reducing it to Oxford philosophy from the Thirties and Forties and its immediate antecedents; that her historical reconstruction is vitiated by lack of awareness of the existence of law-views of morality preceding Christian theology, artful anticipation of secularization in order to fit her picture of modern moral philosophy as the ‘day after’ of Christianity; that Aquinas’s and her own view of natural morality as made of rational moral judgments laws is incompatible with both her predilection for ‘divine law’ instead of plain down-to-earth ‘natural law’; that her strained reconstruction of a Christian-Jewish-Stoic view of morality as law promulgated by God has little to share with any reconstruction of the Biblical moral traditions meeting academic standard and in more detail there is no possible translation of Torah as Law; and that her criticism hits just targets from the old little British world she was familiar with, while leaving Kantian ethics unaffected

The absent-minded prisoner

If one of two rational players is absent-minded for at least three rounds, cooperation in a prisoners dilemma with a finite number of repetitions is possible. If both players are absentminded, even two rounds of absent-mindedness can be enough for cooperation in these rounds and all rounds before. Sufficient conditions for the existence of a cooperative equilibrium are derived, a plausible interpretation of absent-mindedness in the case of many repetitions is given. --absent-mindedness,prisoners dilemma,repeated games

Spartan Daily, June 10, 1946

Volume 34, Issue 151https://scholarworks.sjsu.edu/spartandaily/3780/thumbnail.jp

Should I remember more than you? - On the best response to factor-based strategies -

In this paper we offer a new approach to modeling strategies of bounded complexity, the so-called factor-based strategies. In our model, the strategy of a player in the multi-stage game does not directly map the set of histories to the set of her actions. Instead, the player's perception of is represented by a factor : -> where reflects the "cognitive complexity" of the player. Formally, mapping sends each history to an element of a factor space that represents its equivalence class. The play of the player can then be conditioned just on the elements of the set From the perspective of the original multi-stage game we say that a function from o is a factor of a strategy if there exists a function from to the set of actions of the player such that = In this case we say that the strategy is -factor-asedStationary strategies and strategies played by finite automata and strategies with bounded recall are the most prominent examples of factor-based strategies. In the discounted infinitely repeated game with perfect monitoring, a best reply to a profile of -factor-base strategies need not be a -factor-base strategy. However, if the factor is recursive, namely its value (1 , . . . , ) on a finite string of action profiles ( , . . . , ) is a function of (1 , . . . , - ) and , then for every profile of factor-based strategies there is a best reply that is a pure factor-based strategy. We also study factor-based strategies in the more general case of stochastic games.Bounded rationality, factor-based strategies, bounded recall strategies, finite automata

Social Norms and Monetary Trading

Random matching models have been used in Monetary Economics to argue that money can increase the well being of all agents in the economy. If the model features a finite number of agents it will be shown that there is an equilibrium, analogous to the contagious equilibria described in Kandori (1992), that Pareto dominates the monetary one. However it will be shown also that monetaty equilibria have two important advantages: firstly, they are more plausible in large economies in the sense that the lowest discount factor compatible with monetary equilibria doesn't depend on the population size, which is not the case with contagious equilibria; secondly, it is more stable to finite deviations in the following sense: no matter what the past has been, future play of the equilibrium strategies will give players the same payoff as if the equilibrium strategies were always followed.Monetary trading, social norms

Predicting human cooperation in the Prisoner’s Dilemma using case-based decision theory

In this paper, we show that Case-based decision theory, proposed by Gilboa and Schmeidler (Q J Econ 110(3):605–639, 1995), can explain the aggregate dynamics of cooperation in the repeated Prisoner’s Dilemma, as observed in the experiments performed by Camera and Casari (Am Econ Rev 99:979–1005, 2009). Moreover, we find CBDT provides a better fit to the dynamics of cooperation than does the existing Probit model, which is the first time such a result has been found. We also find that humans aspire to a payoff above the mutual defection outcome but below the mutual cooperation outcome, which suggests they hope, but are not confident, that cooperation can be achieved. Finally, our best-fitting parameters suggest that circumstances with more details are easier to recall. We make a prediction for future experiments: if the repeated PD were run for more periods, then we would be begin to see an increase in cooperation, most dramatically in the second treatment, where history is observed but identities are not. This is the first application of Case-based decision theory to a strategic context and the first empirical test of CBDT in such a context. It is also the first application of bootstrapped standard errors to an agent-based model