Related papers: Pure Nash Equilibria and Best-Response Dynamics in…
We analyze the performance of the best-response dynamic across all normal-form games using a random games approach. The playing sequence -- the order in which players update their actions -- is essentially irrelevant in determining whether…
Generating payoff matrices of normal-form games at random, we calculate the frequency of games with a unique pure strategy Nash equilibrium in the ensemble of $n$-player, $m$-strategy games. These are perfectly predictable as they must…
We consider two-player normal form games where each player has the same finite strategy set. The payoffs of each player are assumed to be i.i.d. random variables with a continuous distribution. We show that, with high probability, the…
We consider finite two-player normal form games with random payoffs. Player A's payoffs are i.i.d. from a uniform distribution. Given p in [0, 1], for any action profile, player B's payoff coincides with player A's payoff with probability p…
This paper examines the convergence behaviour of simultaneous best-response dynamics in random potential games. We provide a theoretical result showing that, for two-player games with sufficiently many actions, the dynamics converge quickly…
If a game has a unique Nash equilibrium, then this equilibrium is arguably the solution of the game from the refinement's literature point of view. However, it might be that for almost all initial conditions, all strategies in the support…
In general, Nash equilibria in normal-form games may require players to play (probabilistically) mixed strategies. We define a measure of the complexity of finite probability distributions and study the complexity required to play Nash…
We analyse the typical structure of games in terms of the connectivity properties of their best-response graphs. Our central result shows that, among games that are `generic' (without indifferences) and that have a pure Nash equilibrium,…
We characterize Nash equilibrium by postulating coherent behavior across varying games. Nash equilibrium is the only solution concept that satisfies the following axioms: (i) strictly dominant actions are played with positive probability,…
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 study the problem of checking for the existence of constrained pure Nash equilibria in a subclass of polymatrix games defined on weighted directed graphs. The payoff of a player is defined as the sum of nonnegative rational weights on…
We use techniques from the statistical mechanics of disordered systems to analyse the properties of Nash equilibria of bimatrix games with large random payoff matrices. By means of an annealed bound, we calculate their number and analyse…
We study how the structure of the interaction graph of a game affects the existence of pure Nash equilibria. In particular, for a fixed interaction graph, we are interested in whether there are pure Nash equilibria arising when random…
We study natural improvement dynamics in weighted congestion games with polynomial latencies of maximum degree $d\geq 1$. We focus on two problems regarding the existence and efficiency of approximate pure Nash equilibria, with a reasonable…
Recently, a new model extending the standard replicator equation to a finite set of players connected on an arbitrary graph was developed in evolutionary game dynamics. The players are interpreted as subpopulations of multipopulations…
Whilst network coordination games and network anti-coordination games have received a considerable amount of attention in the literature, network games with coexisting coordinating and anti-coordinating players are known to exhibit more…
The central result of classical game theory states that every finite normal form game has a Nash equilibrium, provided that players are allowed to use randomized (mixed) strategies. However, in practice, humans are known to be bad at…
We study strategic games on weighted directed graphs, where the payoff of a player is defined as the sum of the weights on the edges from players who chose the same strategy augmented by a fixed non-negative bonus for picking a given…
We analyse the computational complexity of finding Nash equilibria in stochastic multiplayer games with $\omega$-regular objectives. While the existence of an equilibrium whose payoff falls into a certain interval may be undecidable, we…
The game-theoretic risk management framework put forth in the precursor work "Towards a Theory of Games with Payoffs that are Probability-Distributions" (arXiv:1506.07368 [q-fin.EC]) is herein extended by algorithmic details on how to…