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Keywords = multigame

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31 pages, 883 KB  
Article
Pure Bayesian Nash Equilibria for Bayesian Games with Multidimensional Vector Types and Linear Payoffs
by Sébastien Huot and Abbas Edalat
Games 2025, 16(4), 37; https://doi.org/10.3390/g16040037 - 14 Jul 2025
Viewed by 953
Abstract
In this work, we study n-agent Bayesian games with m-dimensional vector types and linear payoffs, also called linear multidimensional Bayesian games. This class of games is equivalent with n-agent, m-game uniform multigames. We distinguish between games that have a [...] Read more.
In this work, we study n-agent Bayesian games with m-dimensional vector types and linear payoffs, also called linear multidimensional Bayesian games. This class of games is equivalent with n-agent, m-game uniform multigames. We distinguish between games that have a discrete type space and those with a continuous type space. More specifically, we are interested in the existence of pure Bayesian Nash equilibriums for such games and efficient algorithms to find them. For continuous priors, we suggest a methodology to perform Nash equilibrium searches in simple cases. For discrete priors, we present algorithms that can handle two-action and two-player games efficiently. We introduce the core concept of threshold strategy and, under some mild conditions, we show that these games have at least one pure Bayesian Nash equilibrium. We illustrate our results with several examples like the double-game prisoner’s dilemma (DGPD), the game of chicken, and the sustainable adoption decision problem (SADP). Full article
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11 pages, 2098 KB  
Article
The Evolution of Cooperation in Multigames with Uniform Random Hypergraphs
by Haozheng Xu, Yiwen Zhang, Xing Jin, Jingrui Wang and Zhen Wang
Mathematics 2023, 11(11), 2409; https://doi.org/10.3390/math11112409 - 23 May 2023
Cited by 9 | Viewed by 2105
Abstract
How to explain the emergence of cooperative behavior remains a significant problem. As players may hold diverse perceptions on a particular dilemma, the concept of multigames has been introduced. Therefore, a multigame is studied within various binary networks. Since group structures are common [...] Read more.
How to explain the emergence of cooperative behavior remains a significant problem. As players may hold diverse perceptions on a particular dilemma, the concept of multigames has been introduced. Therefore, a multigame is studied within various binary networks. Since group structures are common in human society and a person can participate in multiple groups, this paper studies an evolutionary multigame with high-order interaction properties. For this purpose, a uniform random hypergraph is adopted as the network structure, allowing players to interact with all nodes in the same hyperedge. First, we investigate the effect of the multigame payoff matrix differences on the evolution of cooperation and find that increasing the differences in the payoff matrix promotes cooperation on the hypergraph network. Second, we discover that an increase in the average hyperdegree of the hypergraph network promotes network reciprocity, wherein high-hyperdegree nodes influence surrounding nodes to form a cooperator cluster. Conversely, groups with a low hyperdegree are more susceptible to betrayal, leading to a decline in cooperation. Full article
(This article belongs to the Special Issue Game Theory and Complex Networks)
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24 pages, 2594 KB  
Article
The Evolutionary Game of Stakeholders’ Coordination Mechanism of New Energy Power Construction PPP Project: A China Case
by Lei Gao and Zhen-Yu Zhao
Sustainability 2020, 12(3), 1045; https://doi.org/10.3390/su12031045 - 2 Feb 2020
Cited by 37 | Viewed by 4898
Abstract
The government, investors, and the public have formed a dynamic multi-game relationship on the Public-Private-Partnership (PPP) project, but few studies include them in a system to study their win–win solutions. Firstly, we constructed a tripartite game model of the government, investors, and the [...] Read more.
The government, investors, and the public have formed a dynamic multi-game relationship on the Public-Private-Partnership (PPP) project, but few studies include them in a system to study their win–win solutions. Firstly, we constructed a tripartite game model of the government, investors, and the public based on evolutionary game theory. Secondly, the evolutionary process of tripartite strategy behaviors was studied with the system dynamics (SD) model. Finally, the impact of changes in key factors on behavior strategies was studied through sensitivity analysis. The results show the following: (1) In the outsourcing of new energy and power construction PPP projects, the three parties will eventually reach the equilibrium state of {government supervision, public participation, investors effort}, the three parties achieve a win–win situation and the project benefits are the highest at this time, and the public participation will play an important role in promoting the smooth outsourcing of PPP projects. (2) The strategic choices of the government, investors, and the public are sensitive to changes in the corresponding exogenous variables. (3) The security factor plays a crucial role in the choice of public strategy. The public’s choice is not only affected by its own income and cost, but also by the amount of compensation promised by the government and the estimated damage caused by the investor. Full article
(This article belongs to the Special Issue Energy Market Reform and Sustainability)
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24 pages, 431 KB  
Article
Ex Post Nash Equilibrium in Linear Bayesian Games for Decision Making in Multi-Environments
by Abbas Edalat, Samira Hossein Ghorban and Ali Ghoroghi
Games 2018, 9(4), 85; https://doi.org/10.3390/g9040085 - 24 Oct 2018
Cited by 1 | Viewed by 8635
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 [...] Read more.
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. Full article
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26 pages, 379 KB  
Article
Competing in Several Areas Simultaneously: The Case of Strategic Asset Markets
by Manfred Nermuth
Games 2011, 2(2), 209-234; https://doi.org/10.3390/g2020209 - 12 Apr 2011
Viewed by 6687
Abstract
We characterize the structure of Nash equilibria for a certain class of asset market games. In equilibrium, different assets have different returns, and (risk neutral) investors with different wealth hold portfolios with different structures. In equilibrium, an asset’s return is inversely related to [...] Read more.
We characterize the structure of Nash equilibria for a certain class of asset market games. In equilibrium, different assets have different returns, and (risk neutral) investors with different wealth hold portfolios with different structures. In equilibrium, an asset’s return is inversely related to the elasticity of its supply. The larger an investor, the more diversified is his portfolio. Smaller investors do not hold all the assets, but achieve higher percentage returns. More generally, our results can be applied also to other “multi-market games” in which several players compete in several arenas simultaneously, like multi-market Cournot oligopolies, or multiple rent-seeking games. Full article
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