We study the problem of design of strategy-proof in expectation (SP) mechanisms for facility location on a cycle, with the objective of minimizing the sum of costs of n agents. We show that there exists an SP mechanism that attains an approximation ratio of 7/4 with respect to the sum of costs of the agents, thus improving the best known upper bound of 2 - 2/n in the cases of n ≥ 5. The mechanism obtaining the bound randomizes between two mechanisms known in the literature: the Random Dictator (RD) and the Proportional Circle Distance (PCD) mechanism of Meir (2019). To prove the result, we propose a cycle-cutting technique that allows for estimating the problem on a cycle by a problem on a line.

We study discrete two player all-pay auction with complete information. We provide full characterization of mixed strategy Nash equilibria and show that they constitute a subset of Nash equilibria of discrete General Lotto game. We show that equilibria are not unique in general but they are interchangeable and sets of equilibrium strategies are convex. We also show that equilibrium payoffs are unique, unless valuation of at least one of the players is an even integer number. If equilibrium payoffs are not unique, continuum of equilibrium payoffs are possible.

Consider the practical goal of making a desired action profile played, when the planner can only change the payoffs, bound by stringent constraints. Applications include motivating people to choose the closest school, the closest subway station, or to coordinate on a communication protocol or an investment strategy. Employing subsidies and tolls, we adjust the game so that choosing this predefined action profile becomes strictly dominant. Inspired mainly by the work of Monderer and Tennenholtz, where the promised subsidies do not materialise in the not played profiles, we provide a fair and individually rational game adjustment, such that the total outside investments sum up to zero at any profile, thereby facilitating easy and frequent usage of our adjustment without bearing costs, even if some players behave unexpectedly. The resultant action profile itself needs no adjustment. Importantly, we also prove that our adjustment minimises the general transfer among all such adjustments, counting the total subsidising and taxation.

Players are endowed with resources. A player can engage in conflict with others to enlarge his resources. The set of potential conflicts is defined by a contiguity network. Players are farsighted and aim to maximize their resources. They decide on whether to wage war or remain peaceful. The winner of a war takes control of the loser's node and resources; he then decides on whether to wage war against other neighbours, or to stay peaceful. The game ends when either all players choose to be peaceful or when only one player is left.

The aim of the paper is to propose a game-theoretic description of strategies available to players in dialogues. We show how existing dialogical systems can be formalized as Nash-style games, and how the game-theoretic concept of solutions (dominant strategies, Nash equilibrium) can be used to analyse these systems. Our first study, discussed in this article, describes the game DC introduced by Mackenzie.

No abstract available.