In this paper, we show that pure strategy Nash Equilibria in Prime Game and Expansive Game can be linked through an invertible mapping, with which the pure strategy Nash Equilibrium in Prime Game can be easily derived from Expansive Game. Our results provide a tool to solve pure strategy Nash...

We generalize Klumpp, Konrad and Solomon’s model (KKS Model) to multi-contestant sequential Colonel Blotto Games with prize functions where any contestant’s prizes only depend on this contestant’s own number of winning rounds. We show that with weakly monotonic prize functions and CSFs...

We generalize Klumpp, Konrad and Solomon's model (KKS Model) to multi-contestant sequential Colonel Blotto Games with prize functions where any contestant's prizes only depend on this contestant's own number of winning rounds. We show that with weakly monotonic prize functions and CSFs...

We consider a large class of 2-contestant Colonel Blotto games, for which the budget and valuation are both asymmetric between players and the contest success functions are in Tullock form with battle-specific discriminatory power in (0, 1] and battle-and-contestant-specific lobbying...

In this paper, we fully characterize the Nash Equilibrium in the winner-take-all Bertrand Game, showing that a mixed strategy profile is a Nash Equilibrium, if and only if it is a zero operating profit one, and there exist at least two players whose bids are all unprofitable. Compared with...

We consider a large class of 2-contestant Colonel Blotto games, for which the budget and valuation are both asymmetric between players and the contest success functions are in Tullock form with battle-specific discriminatory power in (0, 1] and battle-and-contestant-specific lobbying...

We propose a hide-and-seek game based on compact convex sets in Euclidean space. We show that when the seeker and the hider have a common territory, there exists no pure strategy Nash equilibrium, and the mixed strategy Nash equilibrium of the game are categorized into two types according to the...

In this paper, we study a large class of multi-contestant multi-battle resource allocation contests, where contestants can be asymmetric in terms of both resource budgets and battle valuations, battles can be heterogeneous in terms of both contest success functions and battle valuations, and the...