Suchergebnisse

Stochastic games are have an element of chance: the state of the next round is determined probabilistically depending upon players' actions and the current state. Successful players need to balance the need for short-term payoffs while ensuring future opportunities remain high. The various techniques needed to analyze these often highly non-trivial games are a showcase of attractive mathematics, including methods from probability, differential equations, algebra, and combinatorics. This book presents a course on the theory of stochastic games going from the basics through to topics of modern research, focusing on conceptual clarity over complete generality. Each of its chapters introduces a new mathematical tool - including contracting mappings, semi-algebraic sets, infinite orbits, and Ramsey's theorem, among others - before discussing the game-theoretic results they can be used to obtain. The author assumes no more than a basic undergraduate curriculum and illustrates the theory with numerous examples and exercises, with solutions available online.

"Stochastic games are a mathematical model that is used to study dynamic interactions among agents who in uence the evolution of the environment. These games were rst presented and studied by Lloyd Shapley (1953).1;2 Since Shapley's seminal work, the literature on stochastic games expanded considerably, and the model was applied to numerous areas, such as arm race, shery wars, and taxation"--

The definition of best response for a player in the Nash equilibrium is based on maximizing the expected utility given the strategy of the rest of the players in a game. In this work, we consider stochastic games, that is, games with random payoffs, in which a finite number of players engage only once or at most a limited number of times. In such games, players may choose to deviate from maximizing their expected utility. This is because maximizing expected utility strategy does not address the uncertainty in payoffs. We instead define a new notion of a stochastic superiority best response. This notion of best response results in a stochastic superiority equilibrium in which players choose to play the strategy that maximizes the probability of them being rewarded the most in a single round of the game rather than maximizing the expected received reward, subject to the actions of other players. We prove the stochastic superiority equilibrium to exist in all finite games, that is, games with a finite number of players and actions, and numerically compare its performance to Nash equilibrium in finite-time stochastic games. In certain cases, we show the payoff under the stochastic superiority equilibrium is 70% likely to be higher than the payoff under Nash equilibrium.

This paper analyses the time consistency of open-loop equilibria, in the cases of Nash and Stackelberg behaviour. We define a class of games where the strong time-consistency of the open-loop Nash equilibrium associates with the time consistency of the open-loop Stackelberg equilibrium. We label these games as 'perfect uncontrollable'. We provide one example based on a model of oligopolistic competition in advertising efforts. We also present two oligopoly games where one property holds while the other does not, so that either (i) the open-loop Nash equilibrium is subgame perfect while the stackelberg one is time inconsistent, or (ii) the open-loop Nash and Stackelberg equilibria are only weakly time consistent.

THE TENDENCY OF GOVERNMENT PROGRAMS TO EXPAND WITH TIME WAS EXAMINED AND A LOGICAL EXPLANATION SET FORTH. THE 2 PROGRAMS STUDIED WERE HIGHER EDUCATION AND INCOME MAINTENANCE- BOTH RECEIVE FEDERAL AND STATE FUNDING. THE DATA SHOWED A HIGHLY SIGNIFICANT RELATIONSHIP BETWEEN THE CHANGE IN THE NUMBER OF BENEFICIARIES IN 1 TIME PERIOD AND THE CHANGE IN SPENDING IN THE NEXT.