Auction with aftermarket for budget constrained bidders Departament d’Economia i d’Història Econòmica - IDEA Universitat Autònoma de Barcelona Gustavo Santos Masili Supervisor: Roberto Burguet 07/09/2006

Agenda The model: Auction 1, investment 2 and budget constraints 3 Model solution Equilibria Consumer surplus analysis Auction format choice Conclusions 3- Benoit and Krishna (1998), Burguet and McAfee (2005), Che and Gale (1998) 1- Krishna (2002) 2- Schwartz (1989)

The model c Two firms compete in a Cournot Duopoly with constant marginal cost of production c A patented innovation is auctioned: Its owner may decrease the marg. cost of prod. for the Cournot market depending on the investment applied on its development Firms have initial budget May be used to pay auctioned good and investment

3-Stage market interaction Table: Timetable (3-stage game) 1 st stage (Auction) 2 nd stage (Investment) 3 rd stage (Cournot Market) Winner (Pays θ for patent) Winner chooses I1 chooses q 1 * (I) Loser (pays 0) 2 chooses q 2 * (I) PS: The loser observes θ and I

Does the selling procedure matters?

Firms are symmetric 3 rd stage (Cournot market) 2nd stage (Investment) Cases for budget constraint: Not binding Binding

Firms are symmetric 1 st stage (Auction) Willingness to pay (endogenous): Is the price that makes a firm indifferent between winning and losing the auction Constraint: Not binding: Binding:

Firms are symmetric is the initial budget from which the constraint becomes not binding is continuous in B binding not binding

Firms have different budgets 3 rd and 2 nd stages are similar to previous: Solutions are function of θ i and I i 1 st stage: Same procedure, but now there are 2 WTP when budget is constrained

Equilibria Considering all auction formats and the tie brk rule Symmetric firms: Unique equilibrium Asymmetric firms: There may exist multiple equilibria BR 2 BR 1 WTP 1 WTP 2 NE Which of these equilibria is expected for each auction format? θθ

Subgame perfect equilibrium English auction: θ is the equilibrium Dutch auction: θ is the equilibrium Thus asymmetric case may generate diff. prices according to format What is the implication of this result in the CS?

Consumer surplus Traditionally is In our model, θ also counts as CS θ CS Q P(Q) Q*Q* P(Q * )

Consumer surplus Monotonicity condition (MC) for : For is given by If MC holds the English auction outperforms the Dutch one with respect to the consumer surplus generated in equilibrium Which format is better?

Conclusions For some of the studied cases (i.e. symmetric budget) the auction design does not influence the final outcome For others (i.e. both firms are budget constrained) it may influence English and Dutch auctions, under asymmetry, may lead to different CS

Conclusions Budget constrained bidders may generate: Inefficient allocation Multiplicity of equilibria Endogenous willingness to pay No revenue equivalence between auction formats

So… The regulator can use all this information to design a mechanism that increases the consumer’s satisfaction Auction design matters

Related literature Burguet and McAfee (2005) 1 : N financially constrained bidders compete to enter a Cournot market. θ influences the prod. cost. and investment. High θ inhibits investment? 1- Burguet, R. and P. McAfee (2005). License prices for financially constrained firms. Working Paper.

Related literature Goerre (2003) 2 : Private info+signaling model. Auctions with aftermarket may gen. no RET. Valuation is endogenous and there is a unique equilibrium. 2- Goerre, J. K. (2003). Bidding for the future: signaling in auctions with an aftermarket. Journal of Economic Theory, Vol. 108, pp Economic Theory, Vol. 108, pp