We consider discrete versions of first-price auctions. We present a condition on beliefs about players' values such that, with any fixed finite set of possible bids and sufficiently many players, only bidding the bid closest from below to one's true value survives iterative deletion of bids that...

In this article, we consider how important developments in game theory have contributed to the theory of industrial organization. Our goal is not to survey the theory of industrial organization; rather, we consider the contribution of game theory through a careful discussion of a small number of...

We examine the consequences of vote buying, assuming this practice were allowed and free of stigma. Two parties competing in a binary election may purchase votes in a sequential bidding game via up-front binding payments and/or campaign promises (platforms) that are contingent upon the outcome...

We study all-pay auctions (or wars of attrition), where the highest bidder wins an object, but all bidders pay their bids. We consider such auctions when two bidders alternate in raising their bids and where all aspects of the auction are common knowledge including bidders.valuations. We analyze...

We examine the consequences of lobbying and vote buying, assuming this practice were allowed and free of stigma. Two .lobbyists. compete for the votes of legislators by oþering up-front payments to the legislators in exchange for their votes. We analyze how the lobbyists.budget constraints and...

We examine the consequences of vote buying, assuming this practice were al-lowed and free of stigma. Two parties compete in a binary election and may purchase votes in a sequential bidding game via up-front binding payments and/or campaign promises (platforms) that are contingent upon the...

For a steady state to be a Nash equilibrium the agents have to perfectly observe the actions of others. This paper suggests a solution concept for cases where players observe only an imperfect signal of what the others' actions are. The model is enriched by specifying the signal that each player...

Many important services share the feature that the seller is also the expert who determines who much of the service is needed. Even when the outcomes of such service are observable, it might be difficult for the customer to determine what the expert actually did and whether it was needed. This...