We show that two duelers with similar, lousy shooting skills (a.k.a. Galois duelers) will choose to take turns firing in accordance with the famous Thue-Morse sequence if they greedily demand their chances to fire as soon as the other’s a priori probability of winning exceeds their own. This contrasts with a result from the approximation theory of complex functions that says what more patient d...

In two-player finite-state stochastic games of partial observation on graphs, in every state of the graph, the players simultaneously choose an action, and their joint actions determine a probability distribution over the successor states. The game is played for infinitelymany rounds and thus the players construct an infinite path in the graph. We consider reachability objectives where the firs...

Ellsberg’s experiment involved a gamble with no ambiguity (N) and a gamble where the prize that could be won is objectively known, but the winning probability depends on the (ambiguous) urn’s composition (P). We extend this by including a gamble where the winning probability is objectively known, but the prize depends on the urn’s composition (C), and also gambles where both the probability and...

Behavioral properties of open systems can be formalized as objectives in two-player games. Turn-based games model asynchronous interaction between the players (the system and its environment) by interleaving their moves. Concurrent games model synchronous interaction: the players always move simultaneously. Infinitary winning criteria are considered: Büchi, co-Büchi, and more general parity con...

Intergroup competition has an important impact on the survival and fitness of individuals in group-living species. However, factors influencing the probability of winning an encounter are not fully understood. We studied the influence of numerical advantage and location of the encounter on the chances of winning in eight neighboring groups of Verreaux's sifakas (Propithecus verreauxi), in Kirin...

In binary-utility games, an agent can have only two possible utility values for final states, 1 (win) and 0 (lose). An adversarial binary-utility game is one where for each final state there must be at least one winning and one losing agent. We define an unbiased rational agent as one that seeks to maximize its utility value, but is equally likely to choose between states with the same utility ...

Raz's celebrated Parallel Repetition Theorem shows that the probability of simultaneously winning n independent instances of a two-player one-round game G is exponentially small in n, when the maximum success probability of G is less than 1. Though the statement is intuitive, the proof is rather nontrivial and has found important application in hardness of approximation, cryptography, and commu...