Final answer:
In a game with a discount factor of 0, Player 1 would offer the minimum acceptable amount to Player 2 to maximize their payoff immediately, without factoring in future rounds. Often, this could result in Player 1 keeping the majority of the total available payoff, assuming rational and self-interested players.
Step-by-step explanation:
The question provided relates to game theory, specifically discussing Subgame Perfect Nash Equilibrium (SPNE), which typically involves strategic decision-making where players consider the reactions of other players to their moves. Since the notation δ (delta) is mentioned and assumed to be 0, it appears to refer to the discount factor used in repeated games to give present values of future payoffs. A discount factor of 0 would mean future payoffs are not valued at all, only the immediate payoffs matter.
Considering a discount factor of 0, Player 1, in an SPNE, would seek to maximize their payoff in the first period without concern for future rounds. Player 1 would calculate the smallest offer Player 2 would accept without resorting to a worse alternative, which could be zero payoff. Assuming players are entirely rational and self-interested, Player 1 would offer just enough to ensure that Player 2 accepts, perhaps $1, to maximize Player 1’s payoff, assuming Player 2 accepts the logic that some payoff is better than no payoff at all. Therefore, the maximum equilibrium payoff for Player 1 in the first period would likely be the total available minus the smallest amount Player 1 can offer to Player 2 that will be accepted, which could very well be $9 if the total is $10 and the offer to Player 2 is $1.