Strategic defense and attack for series and parallel reliability systems: reply 1 to comment 1

Kovenock and Roberson's [2011] comment provides initial work which has the potential, when suitably extended, to advance the research frontier. Kovenock and Roberson's paper consists of three sections. The first section is an interesting introduction. The second section, titled ‘Model and Main Result,’ provides no contribution beyond Hausken [2008a]. It consists of Equations (1)–(10) which are equivalent to equations developed by Hausken, and Equation (11) which is equivalent to the utility requirements u???0 and U???0 provided after Equation (17) in Hausken. The third section provides interesting ideas about mixed-strategy equilibria that can be extended in future research.     

Strategic Defense and Attack for Series and Parallel Reliability Systems: Reply to Rejoinder

Kovenock and Roberson's (2012a, b) replication of Hausken’s (2008a) equations and parameter restrictions do not enhance our insight into the defense and attack of reliability systems. This reply intends to fill the remaining understanding gaps.     

STRATEGIC DEFENSE AND ATTACK FOR SERIES AND PARALLEL RELIABILITY SYSTEMS: COMMENT

The contest-theoretic literature on the attack and defense of networks of targets focuses primarily on pure-strategy Nash equilibria. Hausken's 2008 European Journal of Operational Research article typifies this approach, and many of the models in this literature either build upon this model or utilize similar techniques. We show that Hausken's characterization of Nash equilibrium is invalid for much of the parameter space examined and provides necessary conditions for his solution to hold. The complete characterization of mixed-strategy equilibria remains an open problem, although there exist solutions in the literature for special prominent cases.     

A Territorial Conflict: Trade-offs and Strategies

We study a war scenario in which the winner occupies the loser’s territory. Attacking a territory increases the chance of winning, but also causes harm, which in turn decreases the territory’s value (i.e. the reward of winning). This paper highlights the effects of this trade-off on the equilibrium strategies of the warring states in a contest game with endogenous rewards. Providing both static and dynamic models, our analysis captures insights regarding strategic behavior in asymmetric contests with such conflict.     

Evolutionary determinants of war

This paper considers evolutionarily stable decisions about whether to initiate violent conflict rather than accepting a peaceful sharing outcome. Focusing on small sets of players such as countries in a geographically confined area, we use the concept of evolutionary stability in finite populations. We find that players’ evolutionarily stable preferences widen the range of peaceful resource allocations that are rejected in favor of violent conflict, compared to the Nash equilibrium outcomes. Relative advantages in fighting strength are reflected in the equilibrium set of peaceful resource allocations.     

The timing of contests

We develop a simple model to analyze the timing of contests. When the odds of winning a contest are exogenously given – we show that if either the players discount the future or if the total cost of contest is smaller in the future – there exist subgame perfect equilibria where both players settle, anticipating a contest in the future. With endogenous efforts, the aggregate efforts expanded in a contest are smaller if the contest occurs in the future when the relative effort productivities remain constant or diverge over time, thus creating scope for delay in contests. When the effort productivities converge over time, the total efforts may be greater under a future contest. As a consequence, players either settle over the two periods, or else they initiate a contest immediately.