scholarly journals Fuzzy Random Bimatrix Games Based on Possibility and Necessity Measures

2021 ◽  
Vol 25 (6) ◽  
pp. 1024-1030
Author(s):  
Hitoshi Yano ◽  
Keyword(s):  
Quadratic Programming ◽  
Equilibrium Solution ◽  
Bimatrix Games ◽  
Equilibrium Solutions ◽  
Solution Concepts ◽  
Equilibrium Conditions ◽  
Fuzzy Goals ◽  
Random Payoffs ◽  
Quadratic Programming Problems ◽  
Fuzzy Random

In this study, we formulate bimatrix games with fuzzy random payoffs, and introduce equilibrium solution concepts based on possibility and necessity measures. It is assumed that each player has linear fuzzy goals for his/her payoff. To obtain equilibrium solutions based on the possibility and necessity measures, we propose two algorithms in which quadratic programming problems are solved repeatedly until equilibrium conditions are satisfied.

Adversarial Risk Analysis for Auctions Using Mirror Equilibrium and Bayes Nash Equilibrium

2021 ◽  
Author(s):  
Muhammad Ejaz ◽  
Stephen Joe ◽  
Chaitanya Joshi
Keyword(s):  
Nash Equilibrium ◽  
Risk Analysis ◽  
Equilibrium Solution ◽  
Risk Averse ◽  
Prior Work ◽  
Reserve Price ◽  
Solution Concepts ◽  
Risk Seeking ◽  
Sealed Bid ◽  
Sealed Bid Auctions

In this paper, we use the adversarial risk analysis (ARA) methodology to model first-price sealed-bid auctions under quite realistic assumptions. We extend prior work to find ARA solutions for mirror equilibrium and Bayes Nash equilibrium solution concepts, not only for risk-neutral but also for risk-averse and risk-seeking bidders. We also consider bidders having different wealth and assume that the auctioned item has a reserve price.

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