69 research outputs found
Approximate Nash Equilibria via Sampling
We prove that in a normal form n-player game with m actions for each player,
there exists an approximate Nash equilibrium where each player randomizes
uniformly among a set of O(log(m) + log(n)) pure strategies. This result
induces an algorithm for computing an approximate Nash
equilibrium in games where the number of actions is polynomial in the number of
players (m=poly(n)), where is the size of the game (the input size).
In addition, we establish an inverse connection between the entropy of Nash
equilibria in the game, and the time it takes to find such an approximate Nash
equilibrium using the random sampling algorithm
The complexity of interacting automata
This paper studies the interaction of automata of size m. We characterise statistical properties satisfied by random plays generated by a correlated pair of automata with m states each. We show that in some respect the pair of automata can be identified with a more complex automaton of size comparable to mlogm . We investigate implications of these results on the correlated min–max value of repeated games played by automata
Stable Secretaries
We define and study a new variant of the secretary problem. Whereas in the
classic setting multiple secretaries compete for a single position, we study
the case where the secretaries arrive one at a time and are assigned, in an
on-line fashion, to one of multiple positions. Secretaries are ranked according
to talent, as in the original formulation, and in addition positions are ranked
according to attractiveness. To evaluate an online matching mechanism, we use
the notion of blocking pairs from stable matching theory: our goal is to
maximize the number of positions (or secretaries) that do not take part in a
blocking pair. This is compared with a stable matching in which no blocking
pair exists. We consider the case where secretaries arrive randomly, as well as
that of an adversarial arrival order, and provide corresponding upper and lower
bounds.Comment: Accepted for presentation at the 18th ACM conference on Economics and
Computation (EC 2017
Dynamical noise sensitivity for the voter model
We study noise sensitivity of the consensus opinion of the voter model on
finite graphs, with respect to noise affecting the initial opinions and noise
affecting the dynamics.
We prove that the final opinion is stable with respect to small perturbations
of the initial configuration, and is sensitive to perturbations of the dynamics
governing the evolution of the process.
Our proofs rely on the duality relationship between the voter model and
coalescing random walks, and on a precise description of this evolution when we
have coupled dynamics.Comment: 8 pages. Manuscript matching plublished versio
The speed of innovation diffusion in social networks
New ways of doing things often get started through the actions of a few innovators, then diffuse rapidly as more and more people come into contact with prior adopters in their social network. Much of the literature focuses on the speed of diffusion as a function of the network topology. In practice, the topology may not be known with any precision, and it is constantly in flux as links are formed and severed. Here, we establish an upper bound on the expected waiting time until a given proportion of the population has adopted that holds independently of the network structure. Kreindler and Young (2014) demonstrated such a bound for regular networks when agents choose between two options: the innovation and the status quo. Our bound holds for directed and undirected networks of arbitrary size and degree distribution, and for multiple competing innovations with different payoffs
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