W present a diagrammatic method that allows the determination of all Nash equilibria of 2×M nonzero sum games, extending thus the well known diagrammatic techniques for 2 × M zero sum and 2 × 2 nonzero sum games. We show its appropriateness for teaching purposes by analyzing modified versions of the prisoners’ dilemma, the battle of the sexes, as well as of the zero sum game of matching pennies...

We introduce differential game logic (dGL) for specifying and verifying properties of hybrid games, i.e., determined, sequential/dynamic, non-cooperative, zero-sum games of perfect information on hybrid systems that combine discrete and continuous dynamics. Unlike hybrid systems, hybrid games allow choices in the system dynamics to be resolved by different players with different objectives. The...

In this paper we study a two person zero sum stochastic differential game in weak formulation. Unlike the standard literature, which uses strategy type controls, the weak formulation allows us to consider the game with control against control. We shall prove the existence of game value under natural conditions. Another main feature of the paper is that we allow for non-Markovian structure, and ...

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 consider dynamic electromagnetic evasion-interrogation games where the evader can use ferroelectric material coatings to attempt to avoid detection while the interrogator can manipulate the interrogating frequencies to enhance detection. The resulting problem is formulated as a two-player zero-sum dynamic differential game in which the cost functional is based on the expected value of the in...

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...

Abstract   Vertical cooperative (co-op) advertising is typically a cost sharing mechanism and coordinated effort by the channel’s members in order to increase demand and overall profits. In this marketing strategy, the manufacturer shares a fraction of the retailer’s advertising investment. This paper studies the advertising and pricing decisions in a retailer-manufacturer supply chain in which...

In the sequential decision making task known as the best choice problem, n items are presented in a random order one at a time. After each item, the decision maker can determine only their relative ranks. The goal of decision maker is to select the best of all n items without the possibility of recalling previously observed items. Many important business decisions such as choosing a venture par...

Let I1 and I2 be intervals of real numbers. An interval game is played in this way: player 1 secretly selects x ∈ I1 and player 2 secretly and independently selects y ∈ I2. After x and y are revealed, payoffs are given by some predetermined function with domain I1 × I2. The payoff function for a zero sum interval game is a function A : I1 × I2 → R. This is interpreted to mean that the second pl...