Related papers: Conditional gambler's ruin problem with arbitrary …
In this paper we introduce the novel framework of distributionally robust games. These are multi-player games where each player models the state of nature using a worst-case distribution, also called adversarial distribution. Thus each…
Random walks are powerful tools to analyze spatial-temporal patterns produced by living organisms ranging from cells to humans. At the same time, it is evident that these patterns are not completely random but are results of a convolution…
In this paper we unveil some features of a discrete-time quantum walk on the line whose coin depends on the temporal variable. After considering the most general form of the unitary coin operator, we focus on the role played by the two…
We study the two-player coupon-collector competition in which two independent collectors draw one coupon each per round from a set of $d$ equally likely coupon types. Myers and Wilf gave finite formulae for several two-player events and…
We consider a dynamic version of sender-receiver games, where the sequence of states follows an irreducible Markov chain observed by the sender. Under mild assumptions, we provide a simple characterization of the limit set of equilibrium…
We study a robust optimal stopping problem with respect to a set $\cP$ of mutually singular probabilities. This can be interpreted as a zero-sum controller-stopper game in which the stopper is trying to maximize its pay-off while an adverse…
We present a new form of a Parrondo game using discrete-time quantum walk on a line. The two players A and B with different quantum coins operators, individually losing the game can develop a strategy to emerge as joint winners by using…
We study a class of deterministic mean field games on finite and infinite time horizons arising in models of optimal exploitation of exhaustible resources. The main characteristic of our game is an absorption constraint on the players'…
In continuum one-dimensional space, a coupled directed continuous time random walk model is proposed, where the random walker jumps toward one direction and the waiting time between jumps affects the subsequent jump. In the proposed model,…
A new approach to play games quantum mechanically is proposed. We consider two players who perform measurements in an EPR-type setting. The payoff relations are defined as functions of *correlations*, i.e. without reference to classical or…
Random walk models, such as the trap model, continuous time random walks, and comb models exhibit weak ergodicity breaking, when the average waiting time is infinite. The open question is: what statistical mechanical theory replaces the…
In society, mutual cooperation, defection, and asymmetric exploitative relationships are common. Whereas cooperation and defection are studied extensively in the literature on game theory, asymmetric exploitative relationships between…
A binary constraint system game is a two-player one-round non-local game defined by a system of Boolean constraints. The game has a perfect quantum strategy if and only if the constraint system has a quantum satisfying assignment [R. Cleve…
We introduce a "high probability" framework for repeated games with incomplete information. In our non-equilibrium setting, players aim to guarantee a certain payoff with high probability, rather than in expected value. We provide a high…
Classical game theory addresses decision problems in multi-agent environment where one rational agent's decision affects other agents' payoffs. Game theory has widespread application in economic, social and biological sciences. In recent…
We consider quantum XOR games, defined in [11], from the perspective of unitary correlations defined in [7]. We show that Connes' embedding problem has a positive answer if and only if every quantum XOR game has entanglement bias equal to…
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 consider two-player games played over finite state spaces for an infinite number of rounds. At each state, the players simultaneously choose moves; the moves determine a successor state. It is often advantageous for players to choose…
Define a certain gambler's ruin process $\mathbf{X}_{j}, \mbox{ \ }j\ge 0,$ such that the increments $\varepsilon_{j}:=\mathbf{X}_{j}-\mathbf{X}_{j-1}$ take values $\pm1$ and satisfy $P(\varepsilon_{j+1}=1|\varepsilon_{j}=1,…
We obtain expected number of arrivals, probability of arrival, absorption probabilities and expected time before absorption for a modified discrete random walk on the (sub)set of integers. In a [pqrs] random walk the particle can move one…