Optimal Multi-Object Auctions with Risk Averse Buyers

We analyze the optimal auction of multiple non-identical objects when buyers are risk averse. We show that the auction formats that yield the maximum revenue in the risk neutral case are no longer optimal. In particular, selling the goods independently does not maximize the seller's revenue. We observe that seller's incentive for bundling arises solely due to the risk aversion of the buyers. The optimal auction which remains weakly efficient has the following properties: The seller perfectly insures all buyers against the risk of losing the object(s) for which they have high valuation. While the buyers who have high valuation for both objects are compensated if they do not win either object, the buyers who have low valuation for both objects incur a positive payment to the seller in the same event.Multi-object Auctions, Optimal Auctions, Multi-dimensional Screening, Risk Averse Buyers, Bundling

All-pay war

We study a model of war in which the outcome is uncertain not because of luck on the battlefield (as in standard models), but because the involved countries lack information about their opponent. In our model their production and military technologies are common knowledge, but their resources are private information. Each country decides how to allocate its resources to production and warfare. The country with the stronger military wins and receives aggregate production. In equilibrium the country with a comparative advantage in warfare allocates all resources to warfare for low resource levels and follows a non-decreasing concave strategy thereafter. The opponent allocates a constant fraction of its resources to warfare for low resource levels and follows an increasing non-linear strategy thereafter. From an ex ante perspective the country with a comparative advantage in warfare is likely to win the war unless its military technology is much weaker than the opponent’s.Conflict; war; all-pay auction; private information

Selling Goods of Unknown Quality: Forward versus Spot Auctions

We consider an environment where the sale can take place so early that both the seller and the potential buyers have the same uncertainty about the quality of the good. We present a simple model that allows the seller to put the good for sale before or after this uncertainty is resolved, , namely via forward auction or spot auction, respectively. We solve for the equilibrium of these two auctions and then compare the resulting revenues. We also consider the revenue implications of the insurance in forward auctions.Forward Trading, Forward Auctions, Spot Auctions

Selling Goods of Unknown Quality: Forward versus Spot Auctions

We consider an environment where the sale can take place so early that both the seller and the potential buyers have the same uncertainty about the quality of the good. We present a simple model that allows the seller to put the good for sale before or after this uncertainty is resolved, , namely via forward auction or spot auction, respectively. We solve for the equilibrium of these two auctions and then compare the resulting revenues. We also consider the revenue implications of the insurance in forward auctions.Forward Trading, Forward Auctions, Spot Auctions

Optimal Multi-Object Auctions with Risk Averse Buyers

We analyze the optimal auction of multiple non-identical objects when buyers are risk averse. We show that the auction formats that yield the maximum revenue in the risk neutral case are no longer optimal. In particular, selling the goods independently does not maximize the seller's revenue. We observe that seller's incentive for bundling arises solely due to the risk aversion of the buyers. The optimal auction which remains weakly efficient has the following properties: The seller perfectly insures all buyers against the risk of losing the object(s) for which they have high valuation. While the buyers who have high valuation for both objects are compensated if they do not win either object, the buyers who have low valuation for both objects incur a positive payment to the seller in the same event

Optimal Multi-Object Auctions with Risk Averse Buyers

We analyze the optimal auction of multiple non-identical objects when buyers are risk averse. We show that the auction formats that yield the maximum revenue in the risk neutral case are no longer optimal. In particular, selling the goods independently does not maximize the seller's revenue. We observe that seller's incentive for bundling arises solely due to the risk aversion of the buyers. The optimal auction which remains weakly efficient has the following properties: The seller perfectly insures all buyers against the risk of losing the object(s) for which they have high valuation. While the buyers who have high valuation for both objects are compensated if they do not win either object, the buyers who have low valuation for both objects incur a positive payment to the seller in the same event

Selling Goods of Unknown Quality: Forward versus Spot Auctions

We consider an environment where the sale can take place so early that both the seller and the potential buyers have the same uncertainty about the quality of the good. We present a simple model that allows the seller to put the good for sale before or after this uncertainty is resolved, , namely via forward auction or spot auction, respectively. We solve for the equilibrium of these two auctions and then compare the resulting revenues. We also consider the revenue implications of the insurance in forward auctions

Selling Goods of Unknown Quality: Forward versus Spot Auctions

We consider an environment where the sale can take place so early that both the seller and the potential buyers have the same uncertainty about the quality of the good. We present a simple model that allows the seller to put the good for sale before or after this uncertainty is resolved, , namely via forward auction or spot auction, respectively. We solve for the equilibrium of these two auctions and then compare the resulting revenues. We also consider the revenue implications of the insurance in forward auctions

Core Deviation Minimizing Auctions

We study dominant strategy implementable direct mechanisms that minimize the expected surplus from core deviations. Using incentive compatibility conditions, we formulate the core deviation miminimization problem as a calculus of variations problem and then numerically solve it for some particular cases.</p

Selling Goods of Unknown Quality: Forward versus Spot Auctions

We consider an environment where the sale can take place so early that both the seller and the potential buyers have the same uncertainty about the quality of the good. We present a simple model that allows the seller to put the good for sale before or after this uncertainty is resolved, , namely via forward auction or spot auction, respectively. We solve for the equilibrium of these two auctions and then compare the resulting revenues. We also consider the revenue implications of the insurance in forward auctions