A Omitted Proofs

In this section we include all the proofs deferred from the main body. Before we proceed with the proof of Theorem 2.3, let us point out Thus, the theorem follows directly from (6).Corollary 3.1. Suppose that both players employ (OMD) with learning rate η > 0. (t 1) (t 1) (t 1) (t 1) (t 1) (t 1) ( t 1) ( t 1) ( t 1) ( t 1) (t 1) ( t 1) ( t 1) (t 1) ( t 1) (t 1) ( t 1) ( t 1) (t 1) ( t 1) Thus, recalling Definition 2.5, the claim follows from (12) and (13). The sheriff's decision is binding only in the last If the cargo has no illegal items ( i.e. After the placement, players take turns at "firing" at their The game proceeds until either one player has sunk all of the opponent's ships, or At the end of the game, each player's payoff is the The latter modification makes the game general-sum, and incentivizes players to be more risk-averse.