Equilibrium opacity in ultimatum‐offer bargaining

Abstract

We consider ultimatum bargaining between a seller and a buyer of an asset. They know each other's valuation of the asset. Both can defer their decisions to delegates. These delegates have opaque preferences. Seller and buyer choose the opacity of their delegate. For the seller's delegate this choice is restricted to a random reservation price drawn from the set of symmetric two‐point distributions around the seller's true reservation price. The opacity choice of the buyer's delegate is restricted to a random willingness‐to‐pay drawn from the set of symmetric two‐point distribution around the buyer's true willingness‐to‐pay. We characterize the set of pure‐strategy equilibria in their delegation choices. Multiple equilibria arise. Except for two corner solutions, both players will exploit the strategy of opacity. A large set of efficient equilibria exist. For these, opacity choices do not reduce the probability of transacting, but benefit the buyer compared with the no‐delegation equilibrium. We also study the robustness of the results with respect to the player's ability to also resort to a tougher delegate in addition to the opacity choice.

Zero‐intelligence versus human agents: An experimental analysis of the efficiency of Double Auctions and Over‐the‐Counter markets of varying sizes

“…Indeed, negotiations in OTC markets may be interpreted as a combination of bilateral seller-buyer negotiations, hence several of the theoretical features of bilateral and multilateral noncooperative bargaining models apply (seeGomes, 2020;Konrad & Thum, 2020, and references therein).23 For example,Camerer and Hogarth (1999) reviewed 74 experiments with no, low, or high performance-based monetary incentives and found that the modal result has no effect on mean performance.…”

Introduction to the special issue on markets, policies, and economic design: Theory and experiments

“…These results are underpinned by a theoretical model of an OTC model with repeated bargaining under incomplete information. As noted by the authors, negotiations in OTC markets can be viewed as a buyerseller negotiations and thus their model has similarities with others in the literature, for example, Gomes (2020) and Konrad and Thum (2020). For recent insights into the existence issue, see Prokopovych and Yannelis (2021).…”

Opacity in Bargaining Over Public Good Provision

“…There are various strategies for modifying bargaining power at a pre-negotiation stage. The main idea of opacity, as introduced by Konrad and Thum (2020), is that a favorable redistribution of cooperative gains can be achieved by appointing a delegate whose costs or preferences are on average the same as the principal's but may diverge in both directions due to imperfectly observable characteristics. From the responding player's point of view, opacity is beneficial, as a proposer may pursue a less aggressive strategy in order not to put the success of negotiations at risk.…”

“…From the responding player's point of view, opacity is beneficial, as a proposer may pursue a less aggressive strategy in order not to put the success of negotiations at risk. While Konrad and Thum (2020) consider bargaining over a fixed rent, we look at a non-cooperative game of public good provision with the cooperative rent being determined endogenously. This way we bring together the strands of literature on strategic opacity choice and the private provision of public goods.…”