A Boltzmann game is an n-player repeated game, in which Boltzmann machines are employed by players to choose their optimal strategy for each round of the game. Players only have knowledge about the machine they have selected and their own strategy set. Information about other the players and the game’s pay-off function are concealed from all players. Players therefore select their strategies in...

A decision maker faces a decision problem, or a game against nature. For each probability distribution over the state of the world (nature’s strategies), she has a weak order over her acts (pure strategies). We formulate conditions on these weak orders guaranteeing that they can be jointly represented by expected utility maximization with respect to an almost-unique state-dependent utility, tha...

Matrix games like Prisoner’s Dilemma have guided research on social dilemmas for decades. However, they necessarily treat the choice to cooperate or defect as an atomic action. In real-world social dilemmas these choices are temporally extended. Cooperativeness is a property that applies to policies, not elementary actions. We introduce sequential social dilemmas that share the mixed incentive ...

To this point in the class, we have studies stateless games when the payoff matrix is known. We have explored these games as both stage (single shot) games and as repeated games. In this portion of the class, we will continue to study repeated games, but we will assume as little about the problems as possible and we will look at a class of algorithms that allow us to represent states. To be pre...

TheMultipleAttribute DecisionMaking (MADM) problem deals with candidate priority alternatives with respect to various attributes. MADM techniques are popularly used in diverse fields such as engineering, economics, management science, transportation planning, etc. Several approaches have been developed for assessing theweights of MADM problems, e.g., the eigenvector method, ELECTRE, TOPSIS, etc...

This paper deals with the modeling of the strategic allocation of greenhouse gases emission allowances in the EU-wide trading market that results from Kyoto agreement implementation. An M -matrix game is formulated where the players are countries or groups of countries that may have a strategic influence through their allocation of emission allowances and the payoffs are the welfare gains of th...

This paper provides a sufficient condition for the existence and uniqueness of a BayesianNash equilibrium by regarding it as a solution of a variational inequality. The payoff gradient of a game is defined as a vector whose component is a partial derivative of each player’s payoff function with respect to the player’s own action. If the Jacobianmatrix of the payoff gradient is negative definite...

This paper analyzes a multicriteria matrix goal game under entropy environment. Here a new game model known as multicriteria entropy matrix goal Game is formulated. Multiobjective non-linear programming model for each player is established. The concept of Pareto-optimal security strategy assures the property of security in the individual criteria against an opponent’s deviation in strategy; how...

The human-machine function allocation (HFA) strategy of manned submersibles is an important factor that affects the reliability oceanauts. However, uncertainty HFA makes its optimization very complicated. To this end, a non-cooperative game-based method proposed, which transforms multi-objective model mental workload and situation awareness (SA) under into game forms mapping relationship. Menta...

Multilevel games are abstractions of situations where decision makers are distributed in a network environment. In Part I of this paper, the authors present several of the challenging problems that arise in the analysis of multilevel games. In this paper a specific set up is considered where the two games being played are zero-sum games and where the decision makers use the linear reward-inacti...