International Game Theory Review

We analyze the pre- and post-election processes as a two-period game between an incumbent and a challenger. Before the election, in period 1, an incumbent allocates resources into production, fighting with the challenger, and providing public goods, which impact the probability of winning an election. After the election, in period 2 the incumbent may accept the election result, or a coalition or standoff may follow. Six outcomes are that the incumbent wins, the challenger wins, and that a standoff or coalition arises after one of the players wins. We analyze the incumbent’s and challenger’s strategic choices, how these choices depend on a variety of parameters, and the impact of the choices. The analysis is mapped to and tested against empirics of 48 African elections during 2009–2015 which are classified into the six outcomes. To test the model empirically, the correlations between three variables (the incumbent’s fighting and public goods provision and the challenger’s fighting, in period 1) and the six election outcomes are determined for 48 African elections.

This paper analyzes zero sum game involving hybrid controls using viscosity solution theory where both players use discrete as well as continuous controls. We study two problems, one in finite horizon and other in infinite horizon. In both cases, we allow the cost functionals to be unbounded with certain growth, hence the corresponding lower and upper value functions defined in Elliot–Kalton sense can be unbounded. We characterize the value functions as the unique viscosity solution of the associated lower and upper quasi variational inequalities in a suitable function class. Further we find a condition under which the game has a value for both games. The major difficulties arise due to unboundedness of value function. In infinite horizon case we prove uniqueness of viscosity solution by converting the unbounded value function into bounded ones by suitable transformation. In finite horizon case an argument is based on comparison with a supersolution.

We consider an extension of strategic normal form games with a phase before the actual play of the game, where players can make binding offers for transfer of utilities to other players after the play of the game, contingent on the recipient playing the strategy indicated in the offer. Such offers transform the payoff matrix of the original game but preserve its noncooperative nature. The type of offers we focus on here are conditional on a suggested matching offer of the same kind made in return by the receiver. Players can exchange a series of such offers, thus engaging in a bargaining process before a strategic normal form game is played. In this paper, we study and analyze solution concepts for two-player normal form games with such preplay negotiation phase, under several assumptions for the bargaining power of the players, as well as the value of time for the players in such negotiations. We obtain results describing the possible solutions of such bargaining games and analyze the degrees of efficiency and fairness that can be achieved in such negotiation process. We show the similarities and the differences with a variety of frameworks in the literature of bargaining games and games with a preplay phase.

This paper considers a noncooperative transport game of $n$ players on a communication graph. Here players are passenger transportation companies (carriers). Service requests form a Poisson process with an intensity rate matrix $\mathrm{\Lambda }$. Players announce prices for their services and passengers choose an appropriate service by minimizing their individual costs (the ticket price and the expected service time). For each carrier, we solve the pricing problem and define the equilibrium intensity flows in the conditions of competition. A special emphasis is placed on polynomial latency functions.

This paper studies values for cooperative games with transferable utility. Numerous such values can be characterized by axioms of ${\mathrm{\Psi }}_{\epsilon }$-associated consistency, which require that a value is invariant under some parametrized linear transformation ${\mathrm{\Psi }}_{\epsilon }$ on the vector space of cooperative games with transferable utility. Xu et al. [(2008) Linear Algebr. Appl. 428, 1571–1586; (2009) Linear Algebr. Appl. 430, 2896–2897] Xu et al. [(2013) Linear Algebr. Appl. 439, 2205–2215], Hamiache [(2010) Int. Game Theor. Rev. 12, 175–187] and more recently Xu et al. [(2015) Linear Algebr. Appl. 471, 224–240] follow this approach by using a matrix analysis. The main drawback of these articles is the heaviness of the proofs to show that the matrix expression of the linear transformations is diagonalizable. By contrast, we provide quick proofs by relying on the Jordan normal form of the previous matrix.

This paper deals a bimatrix game with payoffs as closed intervals. Existence of equilibrium point of this game is discussed by using suitable interval quadratic programming problem. Further, a methodology is proposed for finding optimal strategies for each player of the game. The methodology is illustrated by numerical example.