Search results for "Mathematica"
showing 10 items of 7971 documents
Recursive and bargaining values
2021
Abstract We introduce two families of values for TU-games: the recursive and bargaining values. Bargaining values are obtained as the equilibrium payoffs of the symmetric non-cooperative bargaining game proposed by Hart and Mas-Colell (1996). We show that bargaining values have a recursive structure in their definition, and we call this property recursiveness. All efficient, linear, and symmetric values that satisfy recursiveness are called recursive values. We generalize the notions of potential, and balanced contributions property, to characterize the family of recursive values. Finally, we show that if a time discount factor is considered in the bargaining model, every bargaining value h…
TUG-OF-WAR, MARKET MANIPULATION, AND OPTION PRICING
2014
We develop an option pricing model based on a tug-of-war game involving the the issuer and holder of the option. This two-player zero-sum stochastic differential game is formulated in a multi-dimensional financial market and the agents try, respectively, to manipulate/control the drift and the volatility of the asset processes in order to minimize and maximize the expected discounted pay-off defined at the terminal date $T$. We prove that the game has a value and that the value function is the unique viscosity solution to a terminal value problem for a partial differential equation involving the non-linear and completely degenerate parabolic infinity Laplace operator.
The erosion of personal norms and cognitive dissonance
2016
ABSTRACTIn this article, we study how personal norms and behaviour interact and evolve when agents try to reduce cognitive dissonance, and how this dynamic relates to Nash equilibrium. We find that in long run, agents play, and norms prescribe, Nash equilibrium in material payoffs (in the absence of norms). Our model captures two main facts: (i) norms erode along the play of the game; (ii) the erosion of norms depends on the set of possible economic choices, so that the policy maker can potentially influence them.
Constrained consensus for bargaining in dynamic coalitional TU games
2011
We consider a sequence of transferable utility (TU) games where, at each time, the characteristic function is a random vector with realizations restricted to some set of values. We assume that the players in the game interact only with their neighbors, where the neighbors may vary over time. The main contributions of the paper are the definition of a robust (coalitional) TU game and the development of a distributed bargaining protocol. We prove the convergence with probability 1 of the bargaining protocol to a random allocation that lies in the core of the robust game under some mild conditions on the players' communication graphs.
Non-cooperative power allocation game with imperfect sensing information for cognitive radio
2012
In this paper, we consider a sensing-based spectrum sharing scenario and present an efficient decentralized algorithm to maximize the total throughput of the cognitive radio users by optimizing jointly both the detection operation and the power allocation, taking into account the influence of the sensing accuracy. This optimization problem can be formulated as a distributed non-cooperative power allocation game, which can be solved by using an alternating direction optimization method. The transmit power budget of the cognitive radio users and the constraint related to the rate-loss of the primary user due to the interference are considered in the scheme. Finally, we use variational inequal…
Efficient Parallel Nash Genetic Algorithm for Solving Inverse Problems in Structural Engineering
2015
A parallel implementation of a game-theory based Nash Genetic Algorithm (Nash-GAs) is presented in this paper for solving reconstruction inverse problems in structural engineering. We compare it with the standard panmictic genetic algorithm in a HPC environment with up to eight processors. The procedure performance is evaluated on a fifty-five bar sized test case of discrete real cross-section types structural frame. Numerical results obtained on this application show a significant achieved increase of performance using the parallel Nash-GAs approach compared to the standard GAs or Parallel GAs.
Values of games with probabilistic graphs
1999
Abstract In this paper we consider games with probabilistic graphs. The model we develop is an extension of the model of games with communication restrictions by Myerson (1977) . In the Myerson model each pair of players is joined by a link in the graph if and only if these two players can communicate directly. The current paper considers a more general setting in which each pair of players has some probability of direct communication. The value is defined and characterized in this context. It is a natural extension of the Myerson value and it turns out to be the Shapley value of a modified game.
REPEATED GAMES WITH PROBABILISTIC HORIZON
2005
Repeated games with probabilistic horizon are defined as those games where players have a common probability structure over the length of the game's repetition, T. In particular, for each t, they assign a probability pt to the event that "the game ends in period t". In this framework we analyze Generalized Prisoners' Dilemma games in both finite stage and differentiable stage games. Our construction shows that it is possible to reach cooperative equilibria under some conditions on the distribution of the discrete random variable T even if the expected length of the game is finite. More precisely, we completely characterize the existence of sub-game perfect cooperative equilibria in finite s…
Stackelberg-Cournot and Cournot equilibria in a mixed markets exchange economy
2012
In this note, we compare two strategic general equilibrium concepts: the Stackelberg-Cournot equilibrium and the Cournot equilibrium. We thus consider a market exchange economy including atoms and a continuum of traders, who behave strategically. We show that, when the preferences of the small traders are represented by Cobb-Douglas utility functions and the atoms have the same utility functions and endowments, the Stackelberg-Cournot and the Cournot equilibrium equilibria coincide if and only if the followers’ best responses functions have a zero slope at the SCE.
Population Games with Vector Payoff and Approachability
2016
This paper studies population games with vector payoffs. It provides a new perspective on approachability based on mean-field game theory. The model involves a Hamilton-Jacobi-Bellman equation which describes the best-response of every player given the population distribution and an advection equation, capturing the macroscopic evolution of average payoffs if every player plays its best response.