Related papers: Optimal strategy in the game Risk or Safety

Game theory serves as a powerful tool for distributed optimization in multi-agent systems in different applications. In this paper we consider multi-agent systems that can be modeled by means of potential games whose potential function…

We prove an explicit upper bound on the amount of entanglement required by any strategy in a two-player cooperative game with classical questions and quantum answers. Specifically, we show that every strategy for a game with n-bit questions…

In this paper, we study a game with positive or plus infinite expectation and determine the optimal proportion of investment for maximizing the limit expectation of growth rate per attempt. With this objective, we introduce a new pricing…

We use three kinds of computations: simulation, numeric, and symbolic, to guide risk-averse gamblers in general, and offer particular advice on how to resolve the famous St. Petersburg paradox.

We consider an extension of the classical Total Store Order (TSO) semantics by expanding it to turn-based 2-player safety games. During her turn, a player can select any of the communicating processes and perform its next transition. We…

We consider zero-sum stochastic games with perfect information and finitely many states and actions. The payoff is computed by a function which associates to each infinite sequence of states and actions a real number. We prove that if the…

In this paper, we present an optimal control problem for stochastic differential games under Markov regime-switching forward-backward stochastic differential equations with jumps and partial information. First, we prove a sufficient maximum…

We consider two-player games over graphs and give tight bounds on the memory size of strategies ensuring safety objectives. More specifically, we show that the minimal number of memory states of a strategy ensuring a safety objective is…

We consider a two-road dynamic routing game where the state of one of the roads (the "risky road") is stochastic and may change over time. This generates room for experimentation. A central planner may wish to induce some of the (finite…

Simple stochastic games are turn-based 2.5-player games with a reachability objective. The basic question asks whether one player can ensure reaching a given target with at least a given probability. A natural extension is games with a…

We present efficient algorithms for computing optimal or approximately optimal strategies in a zero-sum game for which Player I has n pure strategies and Player II has an arbitrary number of pure strategies. We assume that for any given…

Evolutionary game theory assumes that players replicate a highly scored player's strategy through genetic inheritance. However, when learning occurs culturally, it is often difficult to recognize someone's strategy just by observing the…

We introduce the concept of budget games. Players choose a set of tasks and each task has a certain demand on every resource in the game. Each resource has a budget. If the budget is not enough to satisfy the sum of all demands, it has to…

We introduce a two-player game involving two tokens located at points of a fixed set. The players take turns to move a token to an unoccupied point in such a way that the distance between the two tokens is decreased. Optimal strategies for…

N players are randomly fitted with a colored hat (q different colors). All players guess simultaneously the color of their own hat observing only the hat colors of the other N-1 players. The team wins if all players guess right. No…

This paper addresses complexity problems in rational verification and synthesis for multi-player games played on weighted graphs, where the objective of each player is to minimize the cost of reaching a specific set of target vertices. In…

We discuss stochastic dynamics of populations of individuals playing games. Our models possess two evolutionarily stable strategies: an efficient one, where a population is in a state with the maximal payoff (fitness) and a risk-dominant…

Two standard algorithms for approximately solving two-player zero-sum concurrent reachability games are value iteration and strategy iteration. We prove upper and lower bounds of 2^(m^(Theta(N))) on the worst case number of iterations…

Consider a very simple class of (finite) games: after an initial move by nature, each player makes one move. Moreover, the players have common interests: at each node, all the players get the same payoff. We show that the problem of…

Ultimate Tic-Tac-Toe is a variant of the popular Tic-Tac-Toe game. Two players compete to win three aligned "fields," with each field constituting its own miniature tic-tac-toe game. Each move determines which field the next player must…