This paper studies action-based reinforcement learning in finite perfectioninformation games. Restrictions on the valuation updating rule that guarantee that the play eventually converges to a subgame-perfect Nash equilibrium (SPNE) are identified. These conditions are mild enough to contain interesting and plausible learning behavior. We provide two examples of such updating rule that suggest ...

We present a polynomial-time reduction from parity games with imperfect information to safety games with imperfect information. Similar reductions for games with perfect information typically increase the game size exponentially. Our construction avoids such a blow-up by using imperfect information to realise succinct counters which cover a range exponentially larger than their size. In particu...

Kalmar [2, 1928-9] proved that Chess is strictly determined. Von Neumann-Morgenstern [5, 1944] proved the same for any finite two-person zero-sum perfect-information (PI) game. The latter result yields a minimax theorem for (finite) non-zero-sum PI games. Fix a PI, and a player, Ann. Convert this game to a two-person zero-sum game between Ann and the other players (considered as one player), in...

This paper studies action-based reinforcement learning in finite perfectinformation games. Restrictions on the valuation updating rule that that are necessary and sufficient for the play to converge to a subgame-perfect Nash equilibrium (SPNE) are identified. These conditions encompass well-known examples of reinforcement learning and are mild enough to contain other interesting and plausible l...

In generic perfect-information games the unique Subgame-Perfect Equilibrium (SPE) outcome is identical to the one predicted by several rationalizability notions, like Extensive-Form Rationalizability (EFR), the Backward Dominance Procedure (BDP), and Extensive-Form Rationalizability of the Agent form (AEFR). We show that, in contrast, within the general class of perfect information games all th...

The theory of graph games is the foundation for modeling and synthesizing reactive processes. In the synthesis of stochastic processes, we use 2 2 -player games where some transitions of the game graph are controlled by two adversarial players, the System and the Environment, and the other transitions are determined probabilistically. We consider 212 -player games where the objective of the Sys...

Generic extensive form games of perfect information have a unique subgame perfect equilibrium. Nöldeke and Samuelson (1993) show that in a stochastic evolutionary model also non-subgame perfect equilibriumstrategies may well survive in the long run. In a different model of evolution in the agent normal form of generic extensive form games of perfect information Hart (2002) shows that under suit...

The CPR (“cumulative proportional reinforcement”) learning rule stipulates that an agent chooses a move with a probability proportional to the cumulative payoff she obtained in the past with that move. Previously considered for strategies in normal form games (Laslier, Topol and Walliser, Games and Econ. Behav., 2001), the CPR rule is here adapted for actions in perfect information extensive fo...

The paper provides a framework for representing belief-contravening hypotheses in games of perfect information. The resulting t-extended information structures are used to encode the notion that a player has the disposition to behave rationally at a node. We show that there are models where the condition of all players possessing this disposition at all nodes (under their control) is both a nec...

7.1.1 Definitions Definition An extensive game with perfect information 〈N,H, P, Ui〉 has the following components: • A set of N players • A set H of sequences (finite or infinite). each member of H is a history; each component of a history ia an action taken by a player. • P is the player function, P (h) being the player who takes an action after the history h. • Payoff function Ui, i ∈ N After...