Shrinking games and local formulas*1

Shrinking games and local formulas

Gaifman’s normal form theorem showed that every first order sentence of quantifier rank n is equivalent to a Boolean combination of “scattered local sentences”, where the local neighborhoods have radius at most 7n−1. This bound was improved by Lifsches and Shelah to 3 · 4n−1. We use Ehrenfeucht-Fräıssé type games with a “shrinking horizon” to get a spectrum of normal form theorems of the Gaifma...

On Local and Network Games

Evolutionary Games and Local Dynamics

Evolutionary games have been introduced by Maynard Smith and Price [1973] in the early 70’s with the aim to study the stability of populations in time. In the general model, a population consists of finitely many different types that interact randomly with each other, where each interaction leads to fitness payoffs for each of the types involved. Consequently, the population distribution over t...

Local-Effect Games

We present a new class of games, local-effect games (LEGs), which exploit structure in a different way from other compact game representations studied in A I . We show both theoretically and empirically that these games often (but not always) have pure-strategy Nash equilibria. Finding a potential function is a good technique for finding such equilibria. We give a complete characterization of w...

Quantum Non-Local Games

This work investigates upon the idea of using quantum entanglement in reference to non-local(NL) games. We begin with the definition of a non-local game and study it’s importance in context to the advantage gained over playing the game classically i.e. when no entanglement is involved. For certain NL games, like the XOR games, the gap between the value of the game(maximum success probability) p...