16,918 research outputs found
The structure of pairing strategies for k-in-a-row type games
In Maker-Breaker positional games two players, Maker and Breaker, play on a finite or infinite board with the goal of claiming or preventing the opponent from getting a finite winning set, respectively. For different games there are several winning strategies for Maker or Breaker. One class of winning strategies is the so-called pairing (paving) strategies. Here, we describe all possible pairing strategies for the 9-in-a-row game. Furthermore, we define a graph of the pairings, containing 194,543 vertices and 532,107 edges, in order to give them a structure. A complete characterization of the graph is also given
Characterising and recognising game-perfect graphs
Consider a vertex colouring game played on a simple graph with
permissible colours. Two players, a maker and a breaker, take turns to colour
an uncoloured vertex such that adjacent vertices receive different colours. The
game ends once the graph is fully coloured, in which case the maker wins, or
the graph can no longer be fully coloured, in which case the breaker wins. In
the game , the breaker makes the first move. Our main focus is on the
class of -perfect graphs: graphs such that for every induced subgraph ,
the game played on admits a winning strategy for the maker with only
colours, where denotes the clique number of .
Complementing analogous results for other variations of the game, we
characterise -perfect graphs in two ways, by forbidden induced subgraphs
and by explicit structural descriptions. We also present a clique module
decomposition, which may be of independent interest, that allows us to
efficiently recognise -perfect graphs.Comment: 39 pages, 8 figures. An extended abstract was accepted at the
International Colloquium on Graph Theory (ICGT) 201
Biased Weak Polyform Achievement Games
In a biased weak polyform achievement game, the maker and the breaker
alternately mark previously unmarked cells on an infinite board,
respectively. The maker's goal is to mark a set of cells congruent to a
polyform. The breaker tries to prevent the maker from achieving this goal. A
winning maker strategy for the game can be built from winning
strategies for games involving fewer marks for the maker and the breaker. A new
type of breaker strategy called the priority strategy is introduced. The
winners are determined for all pairs for polyiamonds and polyominoes up
to size four
Stated versus inferred beliefs: A methodological inquiry and experimental test
If asking subjects their beliefs during repeated game play changes the way those subjects play, using those stated beliefs to evaluate and compare theories of strategic behavior is problematic. We experimentally verify that belief elicitation can alter paths of play in a repeated asymmetric matching pennies game. In this setting, belief elicitation improves the goodness of fit of structural models of belief learning, and the prior beliefs implied by such structural models are both stronger and more realistic when beliefs are elicited than when they are not. These effects are, however, confined to the player type who sees a strong asymmetry between payoff possibilities for her two strategies in the game. We also find that âinferred beliefsâ (beliefs estimated from past observed actions of opponents) can be better predictors of observed actions than the âstated beliefsâ resulting from belief elicitation.beliefs; stated beliefs; belief elicitation; inferred beliefs; estimated beliefs; belief updating; repeated games; experimental methods
Achieving snaky
We prove that the polyomino generally known as snaky is a three-dimensional winner, that it loses on an 8 Ă 8 board, and that its handicap number is at most one
Bargaining Outcomes as the Result of Coordinated Expectations: An Experimental Study of Sequential Bargaining
Experimental studies of two-person sequential bargaining demonstrate that the concept of subgame perfection is not a reliable point predictor of actual behavior. Alternative explanations argue that 1) fairness influences outcomes and 2) that bargainer expectations matter and are likely not to be coordinated at the outset. This paper examines the process by which bargainers in two-person dyads coordinate their expectations on a bargaining convention and how this convention is supported by the seemingly empty threat of rejecting positive but small subgame perfect offers. To organize the data from this experiment, we develop a Markov model of adaptive expectations and bounded rationality. The model predicts actual behavior quite closely.Sequential Bargaining, Experiment, Convention, Fairness, Finite Markov Chain, Bounded Rationality
A Simple Test of Learning Theory?
We report experiments designed to test the theoretical possibility, first discovered by Shapley (1964), that in some games learning fails to converge to any equilibrium, either in terms of marginal frequencies or of average play. Subjects played repeatedly in fixed pairings one of two 3 Ă 3 games, each having a unique Nash equilibrium in mixed strategies. The equilibrium of one game is predicted to be stable under learning, the other unstable, provided payoffs are sufficiently high. We ran each game in high and low payoff treatments. We find that, in all treatments, average play is close to equilibrium even though there are strong cycles present in the data.: Games, Learning, Experiments, Stochastic Fictitious Play, Mixed Strategy Equilibria.
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