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Moving Forward vs. Inflicting Costs in a Random-Walk Model of War

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  • Nakao, Keisuke

Abstract

How do belligerents choose and change their military strategies during war? How do these strategies shape war? To address these questions, we develop a random-walk model of war, where two belligerents fight over "forts" across periods. The random walk represents a battlefront, which moves as the war evolves, resulting in the occupation of more forts for the winning side and less forts for the losing side. Unlike existing models, ours allows the belligerents to choose an action out of moving forward, inflicting costs, and surrender in every battle. We found that equilibrium strategies are monotonic with respect to the walk---a belligerent will punish its opponent if it is sufficiently advantageous and surrender if it is too disadvantageous. Accordingly, the punishment strategy can function to shorten the war. Moreover, a severer punishment tends to make the war even shorter.

Suggested Citation

  • Nakao, Keisuke, 2019. "Moving Forward vs. Inflicting Costs in a Random-Walk Model of War," MPRA Paper 96071, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:96071
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    References listed on IDEAS

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    More about this item

    Keywords

    gambler's ruin; military strategy; random walk;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions
    • F51 - International Economics - - International Relations, National Security, and International Political Economy - - - International Conflicts; Negotiations; Sanctions

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