Biased orientation games

We study biased {\em orientation games}, in which the board is the complete graph $K_n$, and Maker and Breaker take turns in directing previously undirected edges of $K_n$. At the end of the game, the obtained graph is a tournament. Maker wins if the tournament has some property $\mathcal P$ and Breaker wins otherwise. We provide bounds on the bias that is required for a Maker's win and for a Breaker's win in three different games. In the first game Maker wins if the obtained tournament has a cycle. The second game is Hamiltonicity, where Maker wins if the obtained tournament contains a Hamilton cycle. Finally, we consider the $H$-creation game, where Maker wins if the obtained tournament has a copy of some fixed graph $H$

Positional Games

Positional games are a branch of combinatorics, researching a variety of two-player games, ranging from popular recreational games such as Tic-Tac-Toe and Hex, to purely abstract games played on graphs and hypergraphs. It is closely connected to many other combinatorial disciplines such as Ramsey theory, extremal graph and set theory, probabilistic combinatorics, and to computer science. We survey the basic notions of the field, its approaches and tools, as well as numerous recent advances, standing open problems and promising research directions.Comment: Submitted to Proceedings of the ICM 201

About prisoners and dictators: the role of other-self focus, social value orientation, and sterotype primes in shaping cooperative behavior.

Six experiments examined the effects of person factors (i.e., social value orientation and consistency) and situation factors (i.e., stereotype primes) on cooperative behavior in various experimental games. Results indicated that the main and joint influences of person and situation factors on cooperative choices depend on the nature of the game (i.e., prisoner's dilemma or dictator game). Social value orientation, consistency, and primes affect cooperative behavior only in a dictator game, while these factors also lead to rumination about partner's behavioral intentions and personality (and therefore to different cooperative choices) in a prisoner's dilemma game. Differences between these games were explained in terms of the impact they have on other- and self-focus.Choice; Consistency; Dictator game; Effects; Factors; Prisoner's dilemma game; Social Value Orientation; Stereotype Priming; Value;