We submitted this to Economic Theory yesterday, after being rejected at Econometrica. Comments welcomed.
“Splitting a Pie: Mixed Strategies in Bargaining under Complete Information,” with Christopher Connell. We characterize the mixed-strategy equilibria for the bargaining game in which two players simultaneously bid for a share of a pie and receive shares proportional to their bids, or zero if the bids sum to more than 100%. Of particular interest is the symmetric equilibrium in which each player’s support is a single interval. This consists of a convex increasing density $f_1(p)$ on $[{a}, 1-{a}]$ and an atom of probability at $a$, and is unique for given $a \in (0, .5)$. The two outcomes with highest probability are breakdown and a 50-50 split. We use the same approach to characterize all symmetric and asymmetric equilibria over multiple intervals, and all equilibria (such as “hawk-dove”) that mix over a finite set of bids instead of intervals.