One of the simplest and yet non-trivial results in foundations of mathematics, which can be presented to high school pupils, is Theorem of Zermelo on the determinacy of the game of chess [14]: either Black or White has a winning strategy, or both players have strategies to achieve a draw. The proof smoothly generalizes the problem to all nite games with perfect information, and reveals an algor...

This paper defines the extensive form correlated equilibrium (EFCE) for extensive games with perfect recall. The EFCE concept extends Aumann’s strategic-form correlated equilibrium (CE). Before the game starts, a correlation device generates a move for each information set. This move is recommended to the player only when the player reaches the information set. In two-player perfect-recall exte...

We consider a class of two-player dynamic stochastic nonzero-sum games where the state transition and observation equations are linear, and the primitive random variables are Gaussian. Each controller acquires possibly different dynamic information about the state process and the other controller’s past actions and observations. This leads to a dynamic game of asymmetric information among the c...

Monte Carlo Tree Search (MCTS) has recently been successfully used to create strategies for playing imperfect-information games. Despite its popularity, there are no theoretic results that guarantee its convergence to a well-defined solution, such as Nash equilibrium, in these games. We partially fill this gap by analysing MCTS in the class of zero-sum extensive-form games with simultaneous mov...

The evolutionary basis for predicting the backwards induction solution in generic ̄nite extensive-form games with perfect information is examined. Evolution is modelled using the replicator dynamic in combination with rare mutations that introduce a small change in the proportion of each strategy. The criterion for our judgement is whether this dynamic stabilizes over time at the subgame perfec...