Related papers: A duality principle for selection games
We introduce a new two-player game on graphs, in which players alternate choosing vertices until the set of chosen vertices forms a dominating set. The last player to choose a vertex is the winner. The game fits into the scheme of several…
Social dilemmas are situations in which collective welfare is at odds with individual gain. One widely studied example, due to the conflict it poses between human behaviour and game theoretic reasoning, is the Traveler's Dilemma. The…
This article presents a unified probabilistic framework that allows both rational and irrational decision making to be theoretically investigated and simulated in classical and quantum games. Rational choice theory is a basic component of…
We study a model of a competing population of N adaptive agents, with similar capabilities, repeatedly deciding whether to attend a bar with an arbitrary cutoff L. Decisions are based upon past outcomes. The agents are only told whether the…
A decision maker observes the evolving state of the world while constantly trying to predict the next state given the history of past states. The ability to benefit from such predictions depends not only on the ability to recognize patters…
We consider a version of large population games whose players compete for resources using strategies with adaptable preferences. The system efficiency is measured by the variance of the decisions. In the regime where the system can be…
Game theory is usually considered applied mathematics, but a few game-theoretic results, such as Borel determinacy, were developed by mathematicians for mathematics in a broad sense. These results usually state determinacy, i.e. the…
Relying on configuration spaces and equivariant topology, we study a general "cooperative envy-free division problem". A group of players want to cut a "cake" $I=[0,1]$ and divide among themselves the pieces in an envy-free manner. Once the…
In this paper we consider a distributed coordination game played by a large number of agents with finite information sets, which characterizes emergence of a single dominant attribute out of a large number of competitors. Formally, $N$…
Research has shown that the addition of abstention as an option transforms social dilemmas to rock-paper-scissor type games, where defectors dominate cooperators, cooperators dominate abstainers (loners), and abstainers (loners), in turn,…
In this paper we introduce a qualitative decision and game theory based on belief (B) and desire (D) rules. We show that a group of agents acts as if it is maximizing achieved joint goals.
We study a combinatorial game derived from a problem in the German National Mathematics Competition. In this game, two players take turns removing numbers from a finite set of natural numbers, aiming to satisfy a certain divisibility…
Inspired by the theory of desirable gambles that is used to model uncertainty in the field of imprecise probabilities, I present a theory of desirable things. Its aim is to model a subject's beliefs about which things are desirable. What…
A group of $n$ agents with numerical preferences for each other are to be assigned to the $n$ seats of a dining table. We study two natural topologies:~circular (cycle) tables and panel (path) tables. For a given seating arrangement, an…
We consider an odd-sized "jury", which votes sequentially between two states of Nature (say A and B, or Innocent and Guilty) with the majority opinion determining the verdict. Jurors have private information in the form of a signal in…
We consider a game with two players, consisting of a number of rounds, where the first player to win $n$ rounds becomes the overall winner. Who wins each individual round is governed by a certain urn having two types of balls (type 1 and…
Minority game is a model of heterogeneous players who think inductively. In this game, each player chooses one out of two alternatives every turn and those who end up in the minority side wins. It is instructive to extend the minority game…
We examine a two-person game we call Will-Testing in which the strategy space for both players is a real number. It has no equilibrium. When an infinitely large set of players plays this in all possible pairings, there is an equilibrium for…
We study a model of consensus decision making, in which a finite group of Bayesian agents has to choose between one of two courses of action. Each member of the group has a private and independent signal at his or her disposal, giving some…
We design two mechanisms that ensure that the majority preferred option wins in all equilibria. The first one is a simultaneous game where agents choose other agents to cooperate with on top of the vote for an alternative, thus overcoming…