The game of darts has enjoyed great growth over the past decade with perception moving from that a pub to is regularly scheduled on prime-time television in many countries such as United Kingdom, Germany, Netherlands, and Australia, among others. It involves strategic interactions between two players, but date, literature ignored these interactions. In this paper, we formulate solve dynamic zer...

In this article we consider zero and non-zero sum risk-sensitive average criterion games for semi-Markov processes with a finite state space. For the zero-sum case, under suitable assumptions show that game has value. We also establish existence of stationary saddle point equilibrium. Nash

In this paper we present a Nash equilibrium problem of linear quadratic zero-sum dynamic games for descriptor system. We assume that the players give a linear feedback to the game. For the game with finite planning horizon we derive a differential Riccati type equation. For the game with infinite planning horizon we consider an algebraic Riccati type equation. The connection of the game solutio...

In this paper we present a new algorithm for negotiations in non-zero-sum games. Although games have been studied extensively, most game playing algorithms have been developed under the assumption that players do not communicate. Many real-world problems, however, can be modeled as non-zero-sum games in which players may mutually benefit if they coordinate their actions, which requires negotiat...

The Markov game (also called stochastic game (Filar & Vrieze 1997)) has been adopted as a theoretical framework for multiagent reinforcement learning (Littman 1994). In a Markov game, there are n agents, each facing a Markov decision process (MDP). All agents’ MDPs are correlated through their reward functions and the state transition function. As Markov decision process provides a theoretical ...

We investigate the problem of learning to play the game of rock-paper-scissors. Each player attempts to improve her/his average score by adjusting the frequency of the three possible responses, using reinforcement learning. For the zero sum game the learning process displays Hamiltonian chaos. Thus, the learning trajectory can be simple or complex, depending on initial conditions. We also inves...

One of the earliest solution concepts considered in game theory are saddle points, combinations of actions such that no player can gain by deviating (see, e.g., von Neumann and Morgenstern, 1947). In two-player zero-sum games, every saddle point happens to coincide with the optimal outcome both players can guarantee in the worst case and thus enjoys a very strong normative foundation. Unfortuna...