A Stackelberg equilibrium for a missile procurement problem

This paper deals with a procurement problem of missiles involving the efficient assignment of the missiles to some targets. Within a fixed amount of budget, a leader purchases several types of missiles, by which he aims to damage as much value as possible a follower hides into some facilities later. The effectiveness of the missile depends on the type of missile and facility. A payoff of the game is the expected amount of destroyed value. The problem is generalized as a two-person zero-sum game of distributing discrete resources with a leader and a follower. Our problem is to derive a Stackelberg equilibrium for the game. This type of game has an abundance of applications. The problem is first formulated into an integer programming problem with a non-separable objective function of variables and it is further equivalently transformed into a maximin integer knapsack problem. We propose three exacts methods and an approximation method for an optimal solution.Missile allocation Stackelberg equilibrium Game theory Two-person zero-sum game Integer programming

An approximation for a continuous datum search game with energy constraint

Abstract This paper deals with a datum search game, where a target reveals his position (datum point) at a certain time (datum time) and a pursuer begins the search for the target by distributing his searching effort some time later The target might move in the diffusive fashion from the datum point to evade his pursuer His motion is restricted by its continuity in a two-dimensional space and constraints on its energy and maximum speed The pursuer distributes searching effort to detect the evader under constraints on the amount of effort. A payoff is assumed to be the summation of searching effort weighted by the probability distribution of the target In the previous paper, we formulated the problem as a single-stage two-person zero-sum game on continuous space and continuous time and proposed an upper bound and a lower bound for the value of the game. This paper extends the result and proposes an approximation for the value, noting that a constant-speed motion is crucial for the targe