Person:

Tucker-Foltz, Jamie

We study the classic divide-and-choose method for equitably allocating divisible goods between two players who are rational, self-interested Bayesian agents. The players have additive private values drawn from common priors.

We characterize the structure of optimal divisions in the divide-and-choose game and show how to efficiently compute equilibria. We identify several striking differences between optimal strategies in the cases of known versus unknown preferences. Most notably, the divider has a compelling "diversification" incentive which leads to multiple goods being divided at equilibrium.

We show that the relative utilities of the two players depend on their uncertainties about each other's values and the number of goods. We prove that, when values are independently and identically distributed across players and goods, the chooser is strictly better off for a small number of goods, while the divider is strictly better off for a large number of goods.

We study the classic divide-and-choose method for equitably allocating divisible goods between two players who are rational, self-interested Bayesian agents. The players have additive values for the goods. The prior distributions on those values are common knowledge. We consider both the cases of independent values and values that are correlated across players (as occurs when there is a common-value component).

We describe the structure of optimal divisions in the divide-and-choose game and identify several cases where it is possible to efficiently compute equilibria. An approximation algorithm is presented for the case when the distribution over the chooser’s value for each good follows a normal distribution, along with a randomized approximation algorithm for the case of uniform distributions over intervals.

A mixture of analytic results and computational simulations illuminates several striking differences between optimal strategies in the cases of known versus unknown preferences. Most notably, given unknown preferences, the divider has a compelling “diversification” incentive in creating the chooser’s two options. This incentive leads to multiple goods being divided at equilibrium, quite contrary to the divider’s optimal strategy when preferences are known.

In many contexts, such as buy-and-sell provisions between partners, or in judging fairness, it is important to assess the relative expected utilities of the divider and chooser. Those utilities, we show, depend on the players’ levels of knowledge about each other’s values, the correlations between the players’ values, and the number of goods being divided. Under fairly mild assumptions, we show that the chooser is strictly better off for a small number of goods, while the divider is strictly better off for a large number of goods.

A single seller offers one or more goods to a single buyer. The buyer’s values and the seller’s costs are private information. Each player has a commonly known prior over the other player’s value or cost, supported on a finite set. What is the optimal selling mechanism?

We argue that, despite this question’s importance and apparent simplicity, prior work offers no satisfactory answer. If the seller simply chooses an optimal menu given her realized costs, she fails to exploit her informational advantage. At the other extreme, the optimal trade mechanism that satisfies IC/IR constraints for both parties fails in practice, as it conditions prices on the seller’s unknown costs in an unenforceable way. The seller’s realistic capabilities lie somewhere in between: she may leverage private information but lacks unlimited commitment power.

To bridge this gap, we consider a solution concept built on the realistic assumption that the seller can commit to prices but nothing more. Similar—albeit technically distinct—solution concepts have been studied in the context of auctions with multiple buyers. Our concept proves surprisingly rich even with a single buyer. In our model, the buyer and seller engage in multiple rounds of cheap talk before the seller posts a menu of priced bundles. The buyer then purchases.

We measure value as profit for the seller and consumer surplus for the buyer. We prove that, when there is only one good, such cheap talk cannot improve the welfare of either party. We then demonstrate that cheap talk can be useful when there are (1) multiple goods with additive costs and values, (2) multiple units of a single good with constant marginal cost and diminishing marginal value, (3) interdependent values for a single good, or (4) repeated play of a one-good game. We also show that multiple rounds of communication can yield strictly higher expected profit than a single round.

Conceptually, these results show that in any extension beyond the canonical setting of one seller, one buyer, and one good, cheap talk creates value in bilateral trade. We discuss how realistic factors beyond our stripped-down model combine with cheap talk to enhance this value even further.