Discovering Theorems in Game Theory: Two-Person Games with Unique Pure Nash Equilibrium Payoffs

Tang, Pingzhong; Lin, Fangzhen

Discovering Theorems in Game Theory: Two-Person Games with Unique Pure Nash Equilibrium Payoffs

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Proceedings of the Twenty-First International Joint Conference on Artificial Intelligence. Pages 312-316.

Abstract

In this paper we provide a logical framework for using computers to discover theorems in two-person finite games in strategic form, and apply it to discover classes of games that have unique pure Nash equilibrium payoffs. We consider all possible classes of games that can be expressed by a conjunction of two binary clauses, and our program re-discovered Kats and Thisse's class of weakly unilaterally competitive two-person games, and came up with several other classes of games that have unique pure Nash equilibrium payoffs. It also came up with new classes of strict games that have unique pure Nash equilibria, where a game is strict if for both player different profiles have different payoffs.Pingzhong Tang, Fangzhen Lin

Pingzhong Tang, and Fangzhen Lin. 2009. Discovering Theorems in Game Theory: Two-Person Games with Unique Pure Nash Equilibrium Payoffs. In Proceedings of the Twenty-First International Joint Conference on Artificial Intelligence, IJCAI-09. IJCAI, 312–316. https://ijcai.org/proceedings/2009/60

@inproceedings{ijcai2009p60,
  title     = {Discovering Theorems in Game Theory: Two-Person Games with Unique Pure Nash Equilibrium Payoffs},
  author    = {Tang, Pingzhong and Lin, Fangzhen},
  booktitle = {Proceedings of the Twenty-First International Joint Conference on
               Artificial Intelligence, {IJCAI-09}},
  publisher = {International Joint Conferences on Artificial Intelligence},
  editor    = {Hiroaki Kitano},
  pages     = {312--316},
  year      = {2009},
  url       = {https://ijcai.org/proceedings/2009/60},
}

TY  - CPAPER
TI  - Discovering Theorems in Game Theory: Two-Person Games with Unique Pure Nash Equilibrium Payoffs
AU  - Tang, Pingzhong
AU  - Lin, Fangzhen
T2  - Proceedings of the Twenty-First International Joint Conference on Artificial Intelligence, IJCAI-09
PB  - International Joint Conferences on Artificial Intelligence
PY  - 2009
SP  - 312
EP  - 316
UR  - https://ijcai.org/proceedings/2009/60
ER  -