Strategic Bargaining Analysis

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Suppose the two largest land developers in Rio de Janeiro $($Ipanema Inc. and Copacabana Inc.$)$ are negotiating a government$-$approved plan to allow housing development on the famous Sugarloaf Peak $($P$$o de A$$car$).$ There are a total of $600$ acres to be divided among the two developers. Each developer has a different rate of impatience $($cost of bargaining$)$ as follows: Ipanema $=$ a payoff of $93$ is equal to a payoff of $100$ in the next round; Copacabana $=$ a payoff of $89$ is equal to a payoff of $100$ in the next round.

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a$)$ Calculate the equilibrium first$-$round division of land between the two developers assuming unlimited rounds of bargaining, no surplus decay, and Ipanema making the first offer. How does your equilibrium change if Copacabana makes the first offer?

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b$)$ Which has a greater effect on the equilibrium first offer?

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Circle one:$$ Having a lower discount rate $$or $$Having the first$-$mover advantage

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c$)$ Now assume that there are no longer any costs of negotiation $($no discount rate$)$; however, with each failed round of negotiation, squatters quickly move in to build their own housing at a rate of $100$ acres per round, thereby reducing the amount of available land to be divided among the two developers. The government will not force the squatters to leave once they move in$.$ How does this decay in available land affect the equilibrium first$-$round division of land? Illustrate using a game tree and calculate the equilibrium first offer. Assume Ipanema makes the first offer.