A Note on Ortega Reichert's "A Sequential Game with Information Flow"

Although it was pathbreaking work, Armando Ortega Reichert’s (1968) PhD thesis “Models for Competitive Bidding under Uncertainty” was never published. For reasons of space we publish just Chapter VIII, “A Sequential Game with Information Flow”, which was a seminal analysis of a signalling game.1 This note sets this chapter in context and explains the references it makes to earlier parts of the thesis. The chapter examines a repeated ...rst-price sealed-bid procurement auction in which all bids are reported at the end of each round. At the beginning of each period ...rms privately ...nd out their own costs which are independently drawn from an exponential distribution with unknown parameter, so each ...rm’s costs are correlated across the two rounds. Ortega Reichert shows each bidder has an incentive to bid less aggressively in the ...rst auction than in a one-shot auction in order to alter its opponent’s belief about the unknown parameter, and hence increase its opponent’s estimate of the bidder’s secondperiod costs. 1This chapter was enormously in‡uential in, for example, guiding Milgrom and Roberts’ (1982) analysis of limit pricing (personal communication from Paul Milgrom). It also signi...cantly precedes Spence’s (1972) PhD thesis on signalling games. Ortega Reichert’s thesis develops many other results including about how bidding is affected by bidders’ attitudes to risk, asymmetries in their information, the number of bidders, their uncertainty about the number of other bidders, etc. It also contains an early model of the treasury bill auction market and derives revenue equivalence results similar to those in Vickrey (1962).