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In a zero-sum stochastic game with signals, at each stage, two adversary players take decisions and receive a stage payoff determined by these decisions and a variable called state. The state follows a Markov chain, that is controlled by…

Recently, Press and Dyson have proposed a new class of probabilistic and conditional strategies for the two-player iterated Prisoner's Dilemma, so-called zero-determinant strategies. A player adopting zero-determinant strategies is able to…

When modeling robot interactions as Nash equilibrium problems, it is desirable to place coupled constraints which restrict these interactions to be safe and acceptable (for instance, to avoid collisions). Such games are continuous with…

To take advantage of strategy commitment, a useful tactic of playing games, a leader must learn enough information about the follower's payoff function. However, this leaves the follower a chance to provide fake information and influence…

Through a stochastic control theoretic approach, we analyze reputation games where a strategic long-lived player acts in a sequential repeated game against a collection of short-lived players. The key assumption in our model is that the…

We study a two-player, zero-sum, dynamic game with incomplete information where one of the players is more informed than his opponent. We analyze the limit value as the players play more and more frequently. The more informed player…

We study countably infinite Markov decision processes (MDPs) with real-valued transition rewards. Every infinite run induces the following sequences of payoffs: 1. Point payoff (the sequence of directly seen transition rewards), 2. Total…

In this paper, a time-optimal feedback solution to the game of two cars, for the case where the pursuer is faster and more agile than the evader, is presented. The concept of continuous subsets of the reachable set is introduced to…

Continuous-time assessments of game outcomes in sports have become increasingly common in the last decade. In American football, only discrete-time estimates of play value were possible, since the most advanced public football datasets were…

Markov decision processes (MDPs) are the defacto frame-work for sequential decision making in the presence ofstochastic uncertainty. A classical optimization criterion forMDPs is to maximize the expected discounted-sum pay-off, which…

We have developed a sophisticated statistical model for predicting the hitting performance of Major League baseball players. The Bayesian paradigm provides a principled method for balancing past performance with crucial covariates, such as…

Baseball is one of the few sports in which each team plays a game nearly everyday. For instance, in the baseball league in South Korea, namely the KBO (Korea Baseball Organization) league, every team has a game everyday except for Mondays.…

An active line of research has considered games played on networks in which payoffs depend on both a player's individual decision and also the decisions of her neighbors. Such games have been used to model issues including the formation of…

Semi-Markov model is one of the most general models for stochastic dynamic systems. This paper deals with a two-person zero-sum game for semi-Markov processes. We focus on the expected discounted payoff criterion with state-action-dependent…

We study variants of a stochastic game inspired by backgammon where players may propose to double the stake, with the game state dictated by a one-dimensional random walk. Our variants allow for different numbers of proposals and different…

We study games in which a leader makes a single commitment, and then multiple followers (each with a different utility function) respond. In particular, we study ambiguous commitment strategies in these games, in which the leader may commit…

Repeated games have provided an explanation how mutual cooperation can be achieved even if defection is more favorable in a one-shot game in prisoner's dilemma situation. Recently found zero-determinant strategies have substantially been…

Each of two players, by turns, rolls a dice several times accumulating the successive scores until he decides to stop, or he rolls an ace. When stopping, the accumulated turn score is added to the player account and the dice is given to his…

As a dedicated follower of sports statistics and with the MLB season beginning in late March, I set out to predict how many wins each team would accumulate by the end of the 162 game season. The goal was to build a simulation framework…

We provide a general approach to reformulating any continuous-time stochastic Stackelberg differential game under closed-loop strategies as a single-level optimisation problem with target constraints. More precisely, we consider a…