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1 Information and strategic interaction Assumtions of erfect cometition: (i) (ii) agents (believe they) cannot influence the market rice agents have all relevant information What haens when neither (i) nor (ii) holds? Strategic interaction among a grou of firms where some or all are incomletely informed In articular: What haens when a firm knows more than the others about demand, own costs, etc.? Equilibrium outcome is now also determined by incomletely informed firms beliefs. These beliefs are reresented by subjective robabilities. (i) (ii) Incomlete information in a static model - how beliefs determine the equilibrium in a dynamic model - how beliefs are formed Tore Nilssen Strategic Cometition Lecture 5 Slide

2 Games with incomlete information Perfect Bayesian Equilibrium: Both strategies and beliefs are in equilibrium. Given the strategies in equilibrium, which revised beliefs are consistent with these strategies? Given the beliefs in equilibrium, which strategies are in equilibrium? Two different kinds of roblem: Asymmetric information and the imortance of the uninformed firm observing the informed firm s actions. Symmetric, incomlete information and how there still may be a lot of action even though firms cannot observe each other s actions. Signalling A tyical signalling game: Stage : The informed layer chooses an action (signals) Stage : The uninformed layer observes stage, revises his beliefs about the informed layer, and chooses an action himself. The informed layer s rivate information his tye θ {High, Low} Tore Nilssen Strategic Cometition Lecture 5 Slide

3 The uninformed layer s beliefs about the other s tye: Initial beliefs Pr(High) = H Pr(Low) = L = H Stage : revised beliefs Equilibrium: actions and revised beliefs Searating equilibrium: the action taken by the informed layer at stage deends on his tye. Pooling equilibrium: the action taken by the informed layer at stage is indeendent of his tye. In a ooling equilibrium, the uninformed layer learns nothing about the other layer s tye from observing his stage- action. Beliefs cannot be udated based on that action. In a searating equilibrium, on the other hand, the stage- action reveals the informed layer s tye, and so, based on that action, the uninformed layer can udate his beliefs about the other layer s tye and act accordingly. Tore Nilssen Strategic Cometition Lecture 5 Slide 3

4 First a static model: Price cometition with asymmetric information Two firms. Product differentiation. Price cometition. Product differentiation: A slight increase in a firm s rice causes a slight decrease in its demand and a slight increase in the other firm s demand. D = D (, ); D = D (, ) + + Firm has rivate information about own costs. Both firms know firm s costs. Firm s unit costs: L c = c, with robability x c = L c < H c, with robability ( x) H c Firm only knows the robability distribution ( L c, Firm knows both c and the robability distribution. H c, x) Tore Nilssen Strategic Cometition Lecture 5 Slide 4

5 Tore Nilssen Strategic Cometition Lecture 5 Slide 5 In the case of comlete information: π = ( c )D (, ) ( ) ( ) ( ) 0,, = + = D c D π Best resonse of firm : R ( ). Sloe of the best resonse: sign R ( ) = sign π. ( ) ( ) ( ),, D c D + = π First term ositive Sloe of the best resonse ositive unless D very negative.

6 Equilibrium with comlete information: R ( ) R ( ) Tore Nilssen Strategic Cometition Lecture 5 Slide 6

7 Tore Nilssen Strategic Cometition Lecture 5 Slide 7 The otimum is increasing in c : 0 = + dc c d π π 0 > = = D c dc d π π π H R R L R

8 Firm doesn t know firm s tye. Firm behaves as if confronting an exected firm. L R e R H R R * L* H * Analytically, we find three rices: The rice of the uninformed firm. The rice of the informed firm if it has high costs. The rice of the informed firm if it has low costs. Tore Nilssen Strategic Cometition Lecture 5 Slide 8

9 How is the equilibrium affected by incomlete information? If firm is low-cost, then incomlete information increases the equilibrium rices. If firm is high-cost, then incomlete information reduces the equilibrium rices. Probability of firm being low-cost: x An increase in x reduces equilibrium rices, whether firm is low-cost or high-cost. If firm could choose x, it would want x to be low, whether the firm actually is low-cost or high-cost. The informed firm would like to be believed to have high costs, because that would kee rices high. Tore Nilssen Strategic Cometition Lecture 5 Slide 9

10 Dynamic model Stage : An action by firm that may otentially influence firm s subjective robability that firm is low-cost. Stage : Price cometition with asymmetric information What action? (i) Verifying costs external audit Verification is good for firm if it is high-cost, but not if it is low-cost. (ii) Verification not ossible Model: Two-eriod rice cometition between two firms Period : Price cometition Period : Price cometition Is it ossible for firm to infer firm s cost from firm s rice in stage? In eriod, a high-cost firm would want to set a rice that reveals its cost, while a low-cost firm would not want to reveal its cost. Tore Nilssen Strategic Cometition Lecture 5 Slide 0

11 Signalling game. Could it be ossible for a high-cost firm to set a rice in eriod that is so high that a low-cost firm would not want to mimic it? Yes, because increasing the rice is less costly for a highcost firm than for a low-cost firm. π = ( c )D (, ) π c D = > 0 The effect on firm s rofit of a rice increase deends on the firm s costs. The higher costs are, the stronger is the effect if it is ositive, and the weaker is the effect if it is negative. π low-cost high-cost Tore Nilssen Strategic Cometition Lecture 5 Slide

12 A searating equilibrium is one where firm s rice in eriod deends on its costs. A ooling equilibrium is one where firm s rice in eriod is the same whether it is low-cost or high-cost. L R H R R If firm s rice in eriod reveals its costs, then there is comlete information in eriod. If firm s rice in eriod is uninformative of its costs, then the eriod- game is as in the static model. Firm would want firm to believe it is high-cost, whether this is true or not. Tore Nilssen Strategic Cometition Lecture 5 Slide

13 Firm will only believe firm is a high-cost firm if it sets a rice in eriod that is so high that a low-cost firm would never set it even though, by doing so, it would be considered a high-cost firm in eriod. Thus, in a searating equilibrium, the high-cost bestresonse curve in eriod is further to the right than in the static model. Therefore, the exected best-resonse curve shifts to the right, and all rices are higher in eriod of the two-eriod model than in the static model. An extension: each firm has rivate information about own costs. The result that rices are higher still holds. [Mailath, Simultaneous Signaling in an Oligooly Model, Quart J Econ 989] High-cost firm sets high rice today in order to induce a high rice tomorrow. Puy Dog strategy Tore Nilssen Strategic Cometition Lecture 5 Slide 3

14 Entry deterrence To Dog strategy Two eriods. Firm has rivate information about own costs. Period : Firm is monoolist. It cannot deter entry through caacity investments, etc. Can it deter entry through its eriod- rice? Firm wants firm to believe its costs are low. π c > Eπ 0, < 0 x The interesting case: Entry is rofitable for firm if firm has high costs but not if it has low costs. Reducing the rice is less costly for a low-cost firm than for a high-cost firm. π low-cost high-cost Tore Nilssen Strategic Cometition Lecture 5 Slide 4

15 Comlete information: Period- rice is the monooly rice. Incomlete information: One of two situations may occur. (i) (ii) Low-cost firm sets a rice below its monooly rice, in order to signal its low costs. Searating equilibrium Both tyes of firm set the low-cost monooly rice. Pooling equilibrium Can only haen if firm, without any new information, is deterred from entry. Limit ricing: Price reduction to deter entry. Is limit ricing credible? In case (i), it is. The rice reduction in the searating equilibrium serves to inform the otential entrant that entry is not rofitable because of the resence of a very otent incumbent. In case (ii), it is not. However, the outside firm hasn t learned anything during eriod and therefore chooses to stay out. Tore Nilssen Strategic Cometition Lecture 5 Slide 5

16 What are the welfare consequences of incomlete information? In both cases: Exected rice lower because of incomlete information. In case (i) searating equilibrium entry behaviour is unaffected by incomlete information. Thus, with a searating equilibrium, incomlete information is good for welfare. In case (ii) ooling equilibrium the high-cost firm manages to deter entry by mimicking the low-cost tye. Thus, incomlete information imlies less entry. Total effect on welfare is unclear. What if the entrant does not know its own costs? Suose firms costs are the same, but only firm knows what they are. π < 0 c Firm wants to signal high costs in order to deter entry. Now, the high-cost firm sets rice above monooly in order to deter entry. Puy Dog as entry deterrence. [Harrington, Limit Pricing When the Potential Entrant Is Uncertain of Its Cost Function, Econometrica 986] Tore Nilssen Strategic Cometition Lecture 5 Slide 6

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