Game solver

This page solves games with the solution concept in "Cold Play: Learning Across Bimatrix Games" by Terje Lensberg and Klaus R. Schenk-Hoppé. The paper develops an evolutionary model to predict how experienced agents would play in one-shot games. It is available at

Submit games in the following format:

Number of strategies for Row and Col (max 10 strategies per player)
Payoff matrix for Row (by row)
Payoff matrix for Col (by row)

Example: Battle of the sexes. Click here to see more examples from our paper.

2 2

3 0
0 2

2 0
0 3

Enter game in text box. The solution will appear below after 1-10 seconds.

About solutions

Solutions to games are shown in terms of two matrices. The first matrix displays the payoffs of the game; the pure strategies (strat); the mixed actions (act) of the Row and Col players, and their conjectures (con) about the other player's actions. Pure strategies are named by letters. Lower and upper case denotes (strictly) dominated and undominated strategies, respectively. Nash equilibria in pure strategies are marked with an asterix (*). The second matrix displays the detailed solution to the game, along with the mixed actions and conjectures.

The detailed solution is a bimatrix of the same dimensions as the game. It is a pair P = (P1,P2) of probability distributions (%) on the set of strategy profiles for the game, one probability distribution for each of the two players. For a given player i and strategy profile (s,t), Pi(s,t) is the probability that a randomly chosen agent will solve the game at (s,t) when called upon to play it as player i. For each probability distribution Pi, the mixed actions and conjectures for player i are derived as the marginal distributions of Pi.

The solution engine consists of 200,000 artificial agents who have learned to play one-shot games by natural selection. When an agent is called on to play a game, she is randomly assigned as Row or Col. The agent then solves the game by selecting a strategy profile (s,t). An agent who plays (s,t) as Row does action s, conjecturing that Col will do t, and an agent who plays (s,t) as Col does action t, conjecturing that Row will do s. If the agent selects more than one strategy profile, then each one of them is played with equal probability. A game is solved by taking the average solution across all agents.

Web page created by Terje Lensberg 22.10.2020.