63,121 research outputs found
A note on first-order projections and games
We show how the fact that there is a first-order projection from the problem TC (transitive closure) to some other problem enables us to automatically deduce that a natural game problem, , whose instances are labelled instances of , is complete for PSPACE (via log-space reductions). Our analysis is strongly dependent upon the reduction from TC to being a logical projection in that it fails should the reduction be, for example, a log-space reduction or a quantifier-free first-order translation
Recommended from our members
A Markov chain model for predicting Major League Baseball
In this report, we present a Markov chain model for predicting the scores and the winning team of Major League Baseball (MLB) games. We discuss how a baseball game can be viewed as an infinite horizon discrete-time Markov chain with finite state space. We demonstrate how standard Markov chain theory can be used to obtain analytical solutions for the expected runs and win probability in a given MLB matchup. We improve upon previous models by incorporating pitching and more complex baserunning, and then demonstrate the effect of these changes by comparing our model to historical data. We also discuss computational methods for solving the model. Finally, we test our model on games from the 2015 MLB season.Operations Research and Industrial Engineerin
Flows and Decompositions of Games: Harmonic and Potential Games
In this paper we introduce a novel flow representation for finite games in
strategic form. This representation allows us to develop a canonical direct sum
decomposition of an arbitrary game into three components, which we refer to as
the potential, harmonic and nonstrategic components. We analyze natural classes
of games that are induced by this decomposition, and in particular, focus on
games with no harmonic component and games with no potential component. We show
that the first class corresponds to the well-known potential games. We refer to
the second class of games as harmonic games, and study the structural and
equilibrium properties of this new class of games. Intuitively, the potential
component of a game captures interactions that can equivalently be represented
as a common interest game, while the harmonic part represents the conflicts
between the interests of the players. We make this intuition precise, by
studying the properties of these two classes, and show that indeed they have
quite distinct and remarkable characteristics. For instance, while finite
potential games always have pure Nash equilibria, harmonic games generically
never do. Moreover, we show that the nonstrategic component does not affect the
equilibria of a game, but plays a fundamental role in their efficiency
properties, thus decoupling the location of equilibria and their payoff-related
properties. Exploiting the properties of the decomposition framework, we obtain
explicit expressions for the projections of games onto the subspaces of
potential and harmonic games. This enables an extension of the properties of
potential and harmonic games to "nearby" games. We exemplify this point by
showing that the set of approximate equilibria of an arbitrary game can be
characterized through the equilibria of its projection onto the set of
potential games
- …