Multi-Player Quantum Games

Recently the concept of quantum information has been introduced into game theory. Here we present the first study of quantum games with more than two players. We discover that such games can possess a new form of equilibrium strategy, one which has no analogue either in traditional games or even in two-player quantum games. In these `pure' coherent equilibria, entanglement shared among multiple players enables new kinds of cooperative behavior: indeed it can act as a contract, in the sense that it prevents players from successfully betraying one-another.Comment: 5 pages, 2 figs. Substantial revisons inc. new result

Quantum Matching Pennies Game

A quantum version of the Matching Pennies (MP) game is proposed that is played using an Einstein-Podolsky-Rosen-Bohm (EPR-Bohm) setting. We construct the quantum game without using the state vectors, while considering only the quantum mechanical joint probabilities relevant to the EPR-Bohm setting. We embed the classical game within the quantum game such that the classical MP game results when the quantum mechanical joint probabilities become factorizable. We report new Nash equilibria in the quantum MP game that emerge when the quantum mechanical joint probabilities maximally violate the Clauser-Horne-Shimony-Holt form of Bell's inequality.Comment: Revised in light of referees' comments, submitted to Journal of the Physical Society of Japan, 14 pages, 1 figur

Analysis of two-player quantum games in an EPR setting using geometric algebra

The framework for playing quantum games in an Einstein-Podolsky-Rosen (EPR) type setting is investigated using the mathematical formalism of Clifford geometric algebra (GA). In this setting, the players' strategy sets remain identical to the ones in the classical mixed-strategy version of the game, which is then obtained as proper subset of the corresponding quantum game. As examples, using GA we analyze the games of Prisoners' Dilemma and Stag Hunt when played in the EPR type setting.Comment: 20 pages, no figure, revise

PERFECT RECALL AND PRUNING IN GAMES WITH IMPERFECT INFORMATION 1

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72986/1/j.1467-8640.1996.tb00256.x.pd

N-player quantum games in an EPR setting

The $N$-player quantum game is analyzed in the context of an Einstein-Podolsky-Rosen (EPR) experiment. In this setting, a player's strategies are not unitary transformations as in alternate quantum game-theoretic frameworks, but a classical choice between two directions along which spin or polarization measurements are made. The players' strategies thus remain identical to their strategies in the mixed-strategy version of the classical game. In the EPR setting the quantum game reduces itself to the corresponding classical game when the shared quantum state reaches zero entanglement. We find the relations for the probability distribution for $N$-qubit GHZ and W-type states, subject to general measurement directions, from which the expressions for the mixed Nash equilibrium and the payoffs are determined. Players' payoffs are then defined with linear functions so that common two-player games can be easily extended to the $N$-player case and permit analytic expressions for the Nash equilibrium. As a specific example, we solve the Prisoners' Dilemma game for general $N \ge 2$. We find a new property for the game that for an even number of players the payoffs at the Nash equilibrium are equal, whereas for an odd number of players the cooperating players receive higher payoffs.Comment: 26 pages, 2 figure

What Is True Halving in the Payoff Matrix of Game Theory?

In game theory, there are two social interpretations of rewards (payoffs) for decision-making strategies: (1) the interpretation based on the utility criterion derived from expected utility theory and (2) the interpretation based on the quantitative criterion (amount of gain) derived from validity in the empirical context. A dynamic decision theory has recently been developed in which dynamic utility is a conditional (state) variable that is a function of the current wealth of a decision maker. We applied dynamic utility to the equal division in dove-dove contests in the hawk-dove game. Our results indicate that under the utility criterion, the half-share of utility becomes proportional to a player’s current wealth. Our results are consistent with studies of the sense of fairness in animals, which indicate that the quantitative criterion has greater validity than the utility criterion. We also find that traditional analyses of repeated games must be reevaluated

Strategic Trade Policy as Response to Climate Change?

This paper discusses the political economy of the climate change debate. The objective is to come to a better understanding of why at international levels (e. g. the G8 summit in Heiligendamm) climate change was one of the main topics at the agenda, despite the fact that climate change cannot be solved by only eight participating countries, even if these eight countries are considered as the biggest in the world. The problem of climate change is a supranational one and needs supranational cooperation. Using a strategic trade policy framework, the paper theoretically and from a positive perspective explains why countries like Germany are more engaged in policies related to climate change than other industrial countries, which also have signed the Kyoto Protocol

Psychological Bias as a Driver of Financial Regulation

I propose here the psychological attraction theory of financial regulation—that regulation is the result of psychological biases on the part of political participants—voters, politicians, bureaucrats, and media commentators; and of regulatory ideologies that exploit these biases. Some key elements of the psychological attraction approach are: salience and vividness, omission bias, scapegoating and xenophobia, fairness and reciprocity norms, overconfidence, and mood effects. This approach further emphasizes emergent effects that arise from the interactions of individuals with psychological biases. For example, availability cascades and ideological replicators have powerful effects on regulatory outcomes