Preplay Negotiations with Unconditional Offers of Side Payments in Two-Player Strategic-Form Games: Towards Non-Cooperative Cooperation

I consider strategic-form games with transferable utility extended with a phase of negotiations before the actual play of the game, where players can exchange a series of alternating (turn-based) unilaterally binding offers to each other for incentive payments of utilities after the play, conditional only on the recipients playing the strategy indicated in the offer. Every such offer transforms the game payoff matrix by accordingly transferring the offered amount from the offering player’s payoff to the recipient’s in all outcomes where the indicated strategy is played by the latter. That exchange of offers generates an unbounded-horizon, extensive-form preplay negotiations game, which is the focus of this study. In this paper, I study the case where the players assume that their opponents can terminate the preplay negotiations phase at any stage. Consequently, in their negotiation strategies, the players are guided by myopic rationality reasoning and aim at optimising each of their offers. The main results and findings include a concrete algorithmic procedure for computing players’ best offers in the preplay negotiations phase and using it to demonstrate that these negotiations can generally lead to substantial improvement of the payoffs for both players in the transformed game, but they do not always lead to optimal outcomes, as one might expect.