Econ 100AChapter 14Strategy: Multistage Games*1.Preventing entry: Simultaneous decisions2.Preventing Entry: Sequential decisions3.Creating and using cost advantages4.AdvertisingPreventing EntryConsider a market with either 1 or 2 firms.Neither firm has an advantage that helps it prevent the other firm from entering if both firmssimultaneouslydecide whether to enter.In contrast, anincumbent(firm already in the market)• may have an advantage over a firm deciding whether to enter• because decisions aresequential: The incumbent acts before the potential entrant.Preventing Entry: Simultaneous Decisions2 firms consider opening a gas station at a highway rest stop• Initially there are no gas stations.• There’s enough physical space for at most 2 gas stations.Table 14.1 Simultaneous Entry Game: (a) The market can support two firmsFirm 1Firm 2Do Not Enter EnterDo Not Enter$0$0$3$0Enter$0$3$1$1Both firms enter: Dominant strategy(b) The market can support only one firmFirm 1Firm 2Do Not Enter EnterDo Not Enter$0$0$1$0Enter$0$1-$1-$1Room for Only One FirmThis game is similar to the game ofchicken.*Based on Jeffrey M. Perloff,Microeconomics(© Addison Wesley Longman, 1999). Thesenotes are © Jeffrey M. Perloff.Neither firm has a dominant strategy.What each firm wants to do depends on the other firm’s strategy.In our previously games, firms use apure strategy• each firm chooses an action with certainty• there is only one Nash equilibrium.Here, a firm may employ amixed strategy:it chooses between its possible actions with given probabilities.Pure StrategiesThis game has two Nash equilibria in pure strategies:• Firm 1 enters and Firm 2 does not• Firm 2 enters and Firm 1 does notHow do the players know which Nash equilibrium will result? They don’t.Could collude: the firm that enters could pay the other firm to stay out of the market.Mixed StrategiesThese pure Nash equilibria are unappealing because they call for identical firms to usedifferent strategies.The firms may use the same strategies if their strategies are mixed:• Both firms enter with a probability of a half (flip coin)• there is a Nash equilibrium in mixed strategies• If both firms use this mixed strategy, each of the four outcomes in the payoff matrix inpanel b is equally likelyFirm 1 has:• ¼ chance of earning $1• ¼ chance of losing $1• ½ chance of earning $0• Thus, Firm 1’s expected profit is($1 × ¼) + (-$1 × ¼) + ($0 × ½)=$0Given that Firm 1 uses this mixed strategy, Firm 2 cannot do better by using a pure strategy.• If Firm 2 enters with certainty, it earns $1 half the time and loses -$1 the other half, soits expected profit is $0.• If it stays out with certainty, Firm 2 earns $0.• Thus, both firms playing the mixed strategy or one firm playing one pure strategy ofentering and the other firm playing the pure strategy of not entering are all Nashequilibria.Some games have no pure-strategy Nash equilibrium, so mixed strategies must be usedTheorem(Nash, 1950):Every game with a finite number of firms and a finite number of actions has atleast one Nash equilibrium, which may involve mixed strategies.Preventing Entry: Sequential DecisionsAnincumbentmonopoly firm knows that apotential entrantis considering entering.•Stage 1: incumbent chooses whether to take an action that will prevent the potentialentrant from actually entering the market•Stage 2: potential entrant decides whether to enter, and the firms choose output levels2• Without entry: incumbent earns the monopoly profit• With entry: each firm earns a duopoly profit.We assume that the potential entrant will not bother entering if it just breaks even or losesmoneyWhether the incumbent acts to prevent entry depends on the answer to three questions:• Does it pay for an incumbent to act to prevent entry? (Would it pay a fee to prevententry?)• When can an incumbent prevent entry? (Depends on fixed costs and demand)• What strategic acts and threats of future actions can an incumbent use to prevententry? (Onlycrediblethreats work)To Act or Not to Act?Suppose incumbent can take a strategic action that will prevent the other firm from entering.Does it pay to take action? Three possibilities:•Blockaded entry: Market conditions are such that profitable entry is impossible so noaction necessary•Deterred entry: The incumbent acts to prevent an additional firm from entering becauseitpaysto do so.•Accommodated entry: Doesn’t pay for the incumbent to prevent entry through strategicaction, so it does nothing to prevent entry and reduces its output (or price) from themonopoly to duopoly level to maximize its post-entry profit.Paying to Prevent EntryOne gas station, the incumbent, is already operating at the rest stop.2-stage game:• Stage 1: Incumbent decides whether to pay the landlord of the rest stopbdollars fortheexclusive rightto be the only gas station at the rest stop.• Stage 2: If incumbent doesn’t take this strategic action to prevent entry, the potentialentrant decides whether or not to enter in the second stage.Figure 14.1 shows the game treeEntry isblockadedif the duopoly profit is negative, πd< 0, so that entry doesn’t pay.If πd> 0, entry occurs unless the incumbent engages in strategic action to stop it.Incumbent can prevent entry by payingb, but it may not pay for the incumbent to do so.• It pays if the incumbent’s profit withdeterredentry, πm-b, is greater than πd.•Ifπd>πm-b, it is better off withaccommodatedentry.Fixed Costs, Demand, and Blockaded EntryA second firm can profitably enter this market only if πd> 0 in Figure 14.1.Whether πd> 0 depends on the fixed cost of entering and demand.Assume firms have no variable costs but incur a fixed costFto enter the market.With 2 firms in the market, each firm has revenueRand duopoly profit of πd=R-F.•IfR<F,πd< 0, and the second firm doesn’t enter.• Even though there is not enough demand, given the fixed cost of entry to support 2firms, it is possible that πm>0.3Entry is blockaded only if a firm must incur a fixed cost to enter.IfF= 0, thenR>F, so an entrant can make a profit even if demand is low: πd>0.WithF> 0 and demand so low that there’s room for only one firm in the market, that firm is anatural monopoly.If demand grows, additional firms can enter profitably.We’ve already seen that the number of monopolistically competitive firms in a market dependson how high fixed costs are relative to demand.Because the incumbent is
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