Related papers: Discrete and Continuous Caching Games
We consider a simple dice game, which leads to an intriguing study of multinomial walks, with surprising and seemingly paradoxical properties. The winning and losing probabilities of a general version of the game are investigated via…
Currently the Dempster-Shafer based algorithm and Uniform Random Probability based algorithm are the preferred method of resolving security games, in which defenders are able to identify attackers and only strategy remained ambiguous.…
In this paper we study a linear pursuit differential game described by an infinite system of first-order differential equations in Hilbert space. The control functions of players are subject to geometric constraints. The pursuer attempts to…
Consider a 4-player version of Matching Pennies where a team of three players competes against the Devil. Each player simultaneously says "Heads" or "Tails". The team wins if all four choices match; otherwise the Devil wins. If all team…
This paper considers the distributed strategy design for Nash equilibrium (NE) seeking in multi-cluster games under a partial-decision information scenario. In the considered game, there are multiple clusters and each cluster consists of a…
Player ONE chooses a meager set and player TWO, a nowhere dense set per inning. They play $\omega$ many innings. ONE's consecutive choices must form a (weakly) increasing sequence. TWO wins if the union of the chosen nowhere dense sets…
We introduce a quantum cloning game in which $k$ separate collaborative parties receive a classical input, determining which of them has to share a maximally entangled state with an additional party (referee). We provide the optimal winning…
We consider a two-player game in which the first player (the Guesser) tries to guess, edge-by-edge, the path that second player (the Chooser) takes through a directed graph. At each step, the Guesser makes a wager as to the correctness of…
We investigate the existence of certain types of equilibria (Nash, $\varepsilon$-Nash, subgame perfect, $\varepsilon$-subgame perfect, Pareto-optimal) in multi-player multi-outcome infinite sequential games. We use two fundamental…
We consider {\em bidding games}, a class of two-player zero-sum {\em graph games}. The game proceeds as follows. Both players have bounded budgets. A token is placed on a vertex of a graph, in each turn the players simultaneously submit…
We discuss winning possibilities of players in various variants of cops and robber game played on large random graphs, a testbed for various kinds of network queries, search problems in particular. We explore the use of logic frameworks to…
We present two recursive strategy improvement algorithms for solving simple stochastic games. First we present an algorithm for solving SSGs of degree $d$ that uses at most $O\left(\left\lfloor(d+1)^2/2\right\rfloor^{n/2}\right)$…
We prove new theoretical results about several variations of the cop and robber game on graphs. First, we consider a variation of the cop and robber game which is more symmetric called the cop and killer game. We prove for all $c < 1$ that…
We propose a simple, general and effective technique, Reward Randomization for discovering diverse strategic policies in complex multi-agent games. Combining reward randomization and policy gradient, we derive a new algorithm,…
We begin by reviewing and proving the basic facts of combinatorial game theory. We then consider scoring games (also known as Milnor games or positional games), focusing on the "fixed-length" games for which all sequences of play terminate…
Direct reciprocity is a well-known mechanism that could explain how cooperation emerges and prevails in an evolving population. Numerous prior researches have studied the emergence of cooperation in multiplayer games. However, most of them…
In this paper, we investigate a partially observable zero sum games where the state process is a discrete time Markov chain. We consider a general utility function in the optimization criterion. We show the existence of value for both…
We investigate a variety of cut and choose games, their relationship with (generic) large cardinals, and show that they can be used to characterize a number of properties of ideals and of partial orders: certain notions of distributivity,…
We study the problem of minimizing swap regret in structured normal-form games. Players have a very large (potentially infinite) number of pure actions, but each action has an embedding into $d$-dimensional space and payoffs are given by…
Subset take-away is a two-player game involving a fixed finite set A. Players alternate choosing a proper, non-empty subset of A, with the condition that one may not name a set containing a set that was named earlier. A player unable to…