  In this work, we consider the framework of coalitional Blotto games in which
two players compete against a common adversary by allocating their budgeted
resources across disjoint sets of valued battlefields; the agent that allocates
a higher amount wins the corresponding battlefield value. At the beginning of
the game, the budgets of the agents and the values of the battlefields are
specified. In the first stage, the players are allowed to perform a battlefield
transfer in which one player offloads a number of its battlefields onto the
other player. In the second stage, the adversary observes this transfer and
determines how to allocate their budget accordingly. Finally, in the third
stage, the players and the adversary allocate their budgets to their
battlefields, the game is played, and their payoffs are realized. We provide
necessary and sufficient conditions for the existence of a battlefield transfer
that strictly increases the payoff of each player. We then augment the model,
allowing players to not only transfer subsets of battlefields, but also
portions of their budget, in the first stage. We also provide sufficient
conditions for the existence of a joint transfer of battlefields and budgets.
The results demonstrate that in almost all game instances, both players would
benefit from such a joint transfer.
