...strategies:

In this framework, it is also possible to consider all buyers as utility maximizers, with the additional cost of searching for the lowest price made explicit in the buyer utility functions. In doing so, the search cost for bargain hunters is taken to be zero, while for those buyers that use the any seller strategy, its value is greater than 9#9. The relationship between models of exogenously determined buyer behavior and the endogenous approach which incorporates the cost of information acquisition and explicitly allows for buyer decision-making is further explored in computational settings in Kephart and Greenwald [25]; in the economics literature, see, for example, Burdett and Judd [5] and Wilde and Schwartz [33].

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...9#9.

We assume that buyers' valuations are uncorrelated with their buying strategies.

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...game.

The analysis presented in this section applies to the one-shot version of our model, although the simulation results reported in Sec. 5 focus on repeated settings. We consider the Nash equilibrium of the one-shot game, rather than its iterated counterpart, for at least two reasons, including (i) the Nash equilibrium of the stage game played repeatedly is in fact a Nash equilibrium of the repeated game, and (ii) the Folk Theorem of repeated game theory (see, for example, Fudenberg and Tirole [15]) states that virtually all payoffs in a repeated game correspond to a Nash equilibrium, for sufficiently large values of the discount parameter. Thus, we isolate the stage game Nash equilibrium as an equilibrium of particular interest.

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...59#59,

Precisely, 60#60.

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...59#59.

Precisely, 66#66.

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...model.

This argument rests on the fact that price selection is made within a continuous strategy space; the existence of pure strategy Nash equilibria as an outcome of price discretization is discussed in Appendix A.

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...s:

In Eq. 7, 76#76 is expressed as a function of seller s's scalar price p, given that probability distribution F (p) describes the other sellers' expected prices.

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...myoptimal,

In the game-theoretic literature, this strategy is often referred to as Cournot best-reply dynamics [7]; however, price is being set, rather than quantity.

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...Vohra [12].

For completeness, the details of these algorithms are presented in App. B.

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...price.

It has similarly been observed by Huck, et al. [23] that derivative followers tend towards collusive behavior in models of Cournot duopoly.

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...actions

Technically, there is a continuum of prices in our model. For the purpose of simulating no regret learning, this continuum was discretized into 100 equally sized intervals.

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...121#121.

 Otherwise, v is everywhere replaced by 122#122 in the discussion that follows.

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...133#133.

The value of 91#91 derived in Eq. 9 for the continuous case is applicable in the discrete case, unless 139#139, in which case v is replaced by v' in Eq. 9 (see Foot. 12).

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...regret.

A sequence is remapped if there is a mapping f of the strategy space into itself s.t. for each occurrence of strategy 169#169 in the original sequence, the mapped strategy 170#170 appears in the remapped sequence.

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