Non-cooperative game theory

This is the first draft of the entry “Game Theory” to appear in the Sage Handbook of the Philosophy of Social Science (edited by Ian Jarvie & Jesús Zamora Bonilla), Part III, Chapter 16.game theory, epstemic foundations, incomplete information,epstemic foundations, incomplete information

Social choice theory, game theory, and positive political theory

We consider the relationships between the collective preference and non-cooperative game theory approaches to positive political theory. In particular, we show that an apparently decisive difference between the two approachesthat in sufficiently complex environments (e.g. high-dimensional choice spaces) direct preference aggregation models are incapable of generating any prediction at all, whereas non-cooperative game-theoretic models almost always generate predictionis indeed only an apparent difference. More generally, we argue that when modeling collective decisions there is a fundamental tension between insuring existence of well-defined predictions, a criterion of minimal democracy, and general applicability to complex environments; while any two of the three are compatible under either approach, neither collective preference nor non-cooperative game theory can support models that simultaneously satisfy all three desiderata

Dominant Strategies in Two Qubit Quantum Computations

Nash equilibrium is a solution concept in non-strictly competitive, non-cooperative game theory that finds applications in various scientific and engineering disciplines. A non-strictly competitive, non-cooperative game model is presented here for two qubit quantum computations that allows for the characterization of Nash equilibrium in these computations via the inner product of their state space. Nash equilibrium outcomes are optimal under given constraints and therefore offer a game-theoretic measure of constrained optimization of two qubit quantum computations.Comment: The abstract has been re-written and technical details added to section 5 in version

Formation of coalition structures as a non-cooperative game

Traditionally social sciences are interested in structuring people in multiple groups based on their individual preferences. This pa- per suggests an approach to this problem in the framework of a non- cooperative game theory. Definition of a suggested finite game includes a family of nested simultaneous non-cooperative finite games with intra- and inter-coalition externalities. In this family, games differ by the size of maximum coalition, partitions and by coalition structure formation rules. A result of every game consists of partition of players into coalitions and a payoff? profiles for every player. Every game in the family has an equilibrium in mixed strategies with possibly more than one coalition. The results of the game differ from those conventionally discussed in cooperative game theory, e.g. the Shapley value, strong Nash, coalition-proof equilibrium, core, kernel, nucleolus. We discuss the following applications of the new game: cooperation as an allocation in one coalition, Bayesian games, stochastic games and construction of a non-cooperative criterion of coalition structure stability for studying focal points.Comment: arXiv admin note: text overlap with arXiv:1612.02344, arXiv:1612.0374

Strategic Exploitation of a Common Resource under Environmental Risk

We study the effect of environmental risk on the extraction of a common resource. Using a dynamic and non-cooperative game in which an environmental event impacts both the renewability (the future quantity) and the quality of the resource, we show that the anticipation of such an event has an ambiguous effect on present extraction and the tragedy of the commons. On the one hand, a risk of a reduction in the renewability induces the agents to extract less in the present. On the other hand, a risk of a deterioration in the quality of the resource induces the agents to extract more in the present. We then establish a negative relation between conservative behavior and the tragedy of the commons. In particular, when environmental risk induces conservation (when the risk of less renewability is more important than the risk of quality deterioration), there is a larger decrease in present harvesting under social planning than in the non-cooperative game, and the tragedy of the commons is worsened. The reason is that in a non-cooperative game agents do not internalize the risk that too much extraction creates for others, and, thus, decrease their own extraction too little. The social planner does internalize the effect of conservation on all agents, and decreases harvesting more than in the non-cooperative game, which reduces the risk for the whole group of agents. This disparity in conservation leads to a worsening of the tragedy of the commons in addition to overexposure to the risk of less renewability in the non-cooperative game.Common resource, Conservation, Dynamic games, Environmental risk, Non-cooperative games, Renewable resource exploitation, Stochastic games, Strategic interactions, Tragedy of the Commons, Uncertainty.

The case of two self-enforcing international agreements for environmental protection

Abstract Non-cooperative game theoretical models of self-enforcing international environmental agreements (IEAs) that employ the cartel stability concept of d'Aspremont et al. (1983) frequently use the assumption that countries can sign a single agreement only. We modify the assumption by considering two self-enforcing IEAs. Extending a model of Barrett (1994a) on a single self-enforcing IEA, we demonstrate that there are many similarities between one and two self-enforcing IEAs. But in the case of few countries and high environmental damage we show that two self-enforcing IEA work far better than one self-enforcing IEA in terms of both welfare and environmental equalityKeywords: self-enforcing international environmental agreements; non-cooperative game the- ory; stability; nonlinear optimization

Implementing with veto players: a simple non cooperative game

The paper adapts a non cooperative game presented by Dagan, Serrano and Volij (1997) for bankruptcy problems to the context of TU veto balanced games. We investigate the relationship between the Nash outcomes of a noncooperative game and solution concepts of cooperative games such as the nucleolus, kernel and the egalitarian core.