Computing Bayes-Nash Equilibria through Support Enumeration Methods in Bayesian Two-Player Strategic-Form Games

Ceppi, Sofia; Gatti, Nicola; Basilico, Nicola

doi:10.1109/wi-iat.2009.209

Cited by 12 publications

(10 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To conduct our experimental study, we have used the generator of Π-games proposed in (Ben Amor et al 2019a). This generator, based on GAMUT (Nudelman et al 2004), is available at (Ben Amor et al 2019b) and is essentially based on the approach of (Ceppi, Gatti, and Basilico 2009) for the generation of Bayesian games. The Π-game generator first takes as input the class of the game, the number of degrees in ∆, if necessary the number of players n, the number of actions |A i | and types |Θ i | of player i.…”

Section: Methodsmentioning

confidence: 99%

Ordinal Polymatrix Games with Incomplete Information

Amor

Fargier

Sabbadin

et al. 2020

Proceedings of the Seventeenth International Conference on Principles of Knowledge Representation and Reasoning

View full text Add to dashboard Cite

Possibilistic games with incomplete information (Π-games) constitute a suitable framework for the representation of ordinal games under incomplete knowledge. However, representing a Π-game in standard normal form requires an extensive expression of the utility functions and the possibility distribution, namely, on the product spaces of actions and types. In the present work, we propose a less costly view of Π-games, namely min-based polymatrix Π-games, which allows to concisely specify Π-games with local interactions. This framework allows, for instance, the compact representation of coordination games under uncertainty where the satisfaction of an agent is high if and only if her strategy is coherent with all of her neighbors, the game being possibly only incompletely known to the agents. Then, an important result of this paper is to show that a min-based polymatrix Π-game can be transformed, in polynomial time, into a (complete information) min-based polymatrix game with identical pure Nash equilibria. Finally, we show that the latter family of games can be solved through a MILP formulation. Experiments on variants of the GAMUT problems confirm the feasibility of this approach.

show abstract

Section: Methodsmentioning

confidence: 99%

Ordinal Polymatrix Games with Incomplete Information

Amor

Fargier

Sabbadin

et al. 2020

Proceedings of the Seventeenth International Conference on Principles of Knowledge Representation and Reasoning

View full text Add to dashboard Cite

show abstract

“…In Bayesian games, if the players do not know neither its own type nor the type of the other players, the ex-ante Bayesian Nash Equilibrium (BNE) should be used; if the player knows its own type but not the other players' type, the ex-interim BNE should be used; and if the players know all the players' types, the ex-post BNE should be used. Interested readers are referred to Shoham and Leyton-Brown, (34) Ceppi et al (35) for more information. In Bayesian CPP game, it is assumed that the defender is unique, while the attackers can be various types, such as terrorist, environment activist, disgruntled employee etc.…”

Section: Bayesian Simultaneous Cpp Gamementioning

confidence: 99%

“…Ceppi at el. (35) developed three algorithms for computing ex-interim BNE for 2-player games, namely the B-PNS (based on Support Enumeration), the B-LC (based on Linear Complementarity formulation), and the B-SGC (based on Mixed Integer Linear Programming). In this research, the B-SGC algorithm is employed.…”

Section: Bayesian Simultaneous Cpp Gamementioning

confidence: 99%

See 1 more Smart Citation

Applying a Bayesian Stackelberg game for securing a chemical plant

Zhang

Reniers

2018

Journal of Loss Prevention in the Process Industries

View full text Add to dashboard Cite

In this paper, a Stackelberg defender-adversary game for improving chemical plant protection is proposed, considering multiple types of adversaries. The defender moves first (i.e. forming the "game leader"), setting security alert levels at different entrances of the plant and patrolling levels at different zones. The defender does not exactly know which type of adversary she would face, but knows prior probabilities of occurrence of the different types of adversaries. The adversaries move with full observation of the defender's actions (i.e. forming the "game follower"), choosing which target to attack and deciding how to reach to the target as well as by what level of attack effort. In a case study, we implement the model on a refinery facing threats of suicide bombers and environmental activists.

show abstract

“…These examples are significantly related to a Bayesian Nash equilibrium (BNE), which is an equilibrium concept where all players select their strategies that make their expected utility higher. However, there are not so much computation tools or algorithms specific for the Bayesian game, such as [10,11]. Therefore, the authors think that it is important to facilitate more efficient numerical computation for the Bayesian game.…”

Section: Introductionmentioning

confidence: 99%