Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/219206
Authors: 
Edalat, Abbas
Ghorban, Samira Hossein
Ghoroghi, Ali
Year of Publication: 
2018
Citation: 
[Journal:] Games [ISSN:] 2073-4336 [Volume:] 9 [Year:] 2018 [Issue:] 4 [Pages:] 1-24
Abstract: 
We show that a Bayesian game where the type space of each agent is a bounded set of m-dimensional vectors with non-negative components and the utility of each agent depends linearly on its own type only is equivalent to a simultaneous competition in m basic games which is called a uniform multigame. The type space of each agent can be normalised to be given by the (m − 1)-dimensional simplex. This class of m-dimensional Bayesian games, via their equivalence with uniform multigames, can model decision making in multi-environments in a variety of circumstances, including decision making in multi-markets and decision making when there are both material and social utilities for agents as in the Prisoner's Dilemma and the Trust Game. We show that, if a uniform multigame in which the action set of each agent consists of one Nash equilibrium inducing action per basic game has a pure ex post Nash equilibrium on the boundary of its type profile space, then it has a pure ex post Nash equilibrium on the whole type profile space. We then develop an algorithm, linear in the number of types of the agents in such a multigame, which tests if a pure ex post Nash equilibrium on the vertices of the type profile space can be extended to a pure ex post Nash equilibrium on the boundary of its type profile space in which case we obtain a pure ex post Nash equilibrium for the multigame.
Subjects: 
Multidimensional Bayesian game
multigame
type space partition
Prisoner's Dilemma
Trust Game
Persistent Identifier of the first edition: 
Creative Commons License: 
https://creativecommons.org/licenses/by/4.0/
Document Type: 
Article
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