EconS Asymmetric Information

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1 cons Asymmetric Information ric Dunaway Washington State University eric.dunaway@wsu.edu Industrial Organization ric Dunaway (WSU) cons 425 Industrial Organization 1 / 45

2 Introduction Today, we are going to relax that last assumption of the perfectly competitive market: perfect information. What happens when one rm has more information than the other? This is known as asymmetric information. We saw something similar to this back when we studied menu pricing and vertical di erentiation. ric Dunaway (WSU) cons 425 Industrial Organization 2 / 45

3 Asymmetric Information Let s return to a basic entry deterrence model. Consider a situation where an incumbent monopolist (Player 1) has been operating and they face the possibility of entry by a new rm (Player 2). In the rst stage, a potential entrant decides whether or not to enter a market. If the entrant does not enter, the incumbent remains as a monopolist. If the entrant does enter, the incumbent can choose whether to ght against the entrant or to accomodate their entry. ric Dunaway (WSU) cons 425 Industrial Organization 3 / 45

4 Asymmetric Information ntrant Do Not nter nter Incumbent ntrant 3 0 Fight Incumbent Accomodate ric Dunaway (WSU) cons 425 Industrial Organization 4 / 45

5 Asymmetric Information The incumbent can try to threaten the entrant that they will ght them if they enter, but we know that is not a credible threat. Upon observing entry, choosing accomodate gives the incumbent a higher payo. Thus, in equilibrium, it is best for the incumbent to accomodate the entrant, and for the entrant to enter the market. ric Dunaway (WSU) cons 425 Industrial Organization 5 / 45

6 Asymmetric Information ntrant Do Not nter nter Incumbent ntrant 3 0 Fight Incumbent Accomodate ric Dunaway (WSU) cons 425 Industrial Organization 6 / 45

7 Asymmetric Information What if the incumbent were crazy? Suppose that there was a type of incumbent that likes nothing better than ghting when observing entry into their market. In fact, their payo in this case is their pro t level, 0, plus the extra utility they get from ghting, 2. Would this change our outcome? ric Dunaway (WSU) cons 425 Industrial Organization 7 / 45

8 Asymmetric Information ntrant Do Not nter nter Incumbent ntrant 3 0 Fight Incumbent Accomodate ric Dunaway (WSU) cons 425 Industrial Organization 8 / 45

9 Asymmetric Information ntrant Do Not nter nter Incumbent ntrant 3 0 Fight Incumbent Accomodate ric Dunaway (WSU) cons 425 Industrial Organization 9 / 45

10 Asymmetric Information In this case, a crazy incumbent who loves to ght will do just that. They ght and sacri ce their own pro ts upon observing the entry of another rm. Knowing that the incumbent will ght their entry, the entrant nds it best to not enter the market at all. ric Dunaway (WSU) cons 425 Industrial Organization 10 / 45

11 Asymmetric Information What if the entrant didn t know whether the incumbent were crazy or not? Suppose now that the fact whether the incumbent is crazy or not is private information. There is no way for the entrant to observe this before they decide to enter the market. The entrant, however, knows that the incumbent is crazy with probability θ = 0.1 and not crazy with probability 1 θ = 0.9. This is known as a game of incomplete information. When one player has information that another player does not (asymmetric information), they can use that information to their advantage. ric Dunaway (WSU) cons 425 Industrial Organization 11 / 45

12 Asymmetric Information The entrant must use all of their information to form beliefs. For those of you who have studied probability, the entrant will determine their beliefs based on what they can observe, and update their beliefs using Bayes rule. In this case, the only information that the entrant has is the probability that the incumbent is crazy or not. Let µ denote the entrant s beliefs that the incumbent is crazy. In this case, the entrant s beliefs are the same as the prior probability that the incumbent is crazy, µ = θ = 0.1. ric Dunaway (WSU) cons 425 Industrial Organization 12 / 45

13 Asymmetric Information So what should the entrant do? If they decide not to enter the market, they receive a payo of 0. If they decide to enter the market, they believe that they will receive a payo of 1 with probability 0.1 and a payo of 1 with probability 0.9. We can compare the entrant s expected payo from entering the market with their certain payo of not entering. To calculate their expected payo, we multiply each payo by its respective probability, (π) = 1(µ) + 1(1 µ) = 1(0.1) + 1(0.9) = 0.8 and since 0.8 > 0, the entrant believes they are better o to enter the market, so they do. ric Dunaway (WSU) cons 425 Industrial Organization 13 / 45

14 Asymmetric Information A few things to notice: The entrant s expected utility is based on their beliefs, not the probability that the incumbent is actually crazy. This is important because the beliefs and the probability won t always be the same. If the entrant s belief that the incumbent were crazy was higher, they would actually prefer to not enter the market. In fact, for a belief µ of 1(µ) + 1(1 µ) < 0 it is better to not enter the market at all. µ > 1 2 ric Dunaway (WSU) cons 425 Industrial Organization 14 / 45

15 ven with the possibility that the incumbent is crazy, since the probability of that is low, it s better for the entrant to enter the market. The small chance that the incumbent is actually crazy and will cause them to lose money is o set by the large chance that they are not. Thus, when there is just one possible entrant, it s best for the incumbent to just accomodate entry. What if there was more than one entrant? Suppose now that the incumbent operated in several (20) markets, and each of those markets was going to face a potential entrant. The entrants don t all move at the same time, however. They wait to see how the incumbent reacts to each entrant before them. ric Dunaway (WSU) cons 425 Industrial Organization 15 / 45

16 The rst entrant only has the probability θ = 0.1 that the incumbent is crazy as information. Thus, their belief that the incumbent is crazy is µ 1 = θ = 0.1, and they will decide to enter the market. very other entrant has that prior probability as information, but they also have the incumbent s reaction as information, as well. If the incumbent behaves like they are crazy even if they are not, it will increase the value of µ for the later entrants. The incumbent doesn t actually have to be crazy to make the entrants believe that they are crazy. ric Dunaway (WSU) cons 425 Industrial Organization 16 / 45

17 Suppose that we have an incumbent that isn t crazy. If they accomodate entry into each of their 20 markets, they earn a total payo of 20. Suppose now that this incumbent decided to pretend that they were crazy. The rst entrant tries to enter, and the incumbent ghts them, earning a payo of 0. The second entrant now believes that the monopolist is crazy with 1 2 > µ 2 > µ 1 = θ. They still enter and the incumbent ghts again, earning a payo of 0. ric Dunaway (WSU) cons 425 Industrial Organization 17 / 45

18 The third entrant now sees that the incumbent has fought twice, and they might have a pretty strong belief that the incumbent is actually crazy. They now believe that the monopolist is crazy with µ 3 > 1 2 > µ 2 > µ 1 = θ. They decide to not enter the market and the monopolist earns a payo of 3. All the other entrants agree with the third entrant and believe that the incumbent is crazy and do not enter the market. The incumbent s total payo is (3) = 48 which is much higher than accomodating entry for all 20 entrants. ric Dunaway (WSU) cons 425 Industrial Organization 18 / 45

19 This is known as the Chain-Store paradox. An incumbent would accomodate entry for a low number of entrants, but ght entry for a large number of entrants. ectively, the monopolist sent a signal to later entrants and tried to convince them that they were crazy, even though they took losses in the rst few markets. This is why the di erence between probability and beliefs is so important. Probability is just one facet that goes into determining player beliefs in a game of incomplete information. Let s look at another example. ric Dunaway (WSU) cons 425 Industrial Organization 19 / 45

20 Consider the following two-stage game. In the rst stage, an incumbent monopolist is able to set a high price or a low price and sell to a market. In the second stage, a potential entrant is able to observe the incumbent s price in the rst stage, and then decide whether to enter the market or not. The entrant does not know the incumbent s costs. With probability θ, the incumbent has high costs, and with probability 1 θ, the incumbent has low costs. Remember that when costs are lower, prices (and pro t margin) decrease. The entrant only wants to enter the market if the incumbent has high costs. ric Dunaway (WSU) cons 425 Industrial Organization 20 / 45

21 If the incumbent has high costs, it s better for them to set a high price in the rst stage. Likewise, if they have low costs, it s better for them to set a low price. We can denote the monopolist s pro ts as a function of the price they charge. A high cost, high price monopolist earns π I H (p H ) = π H and a low cost, low price monopolist earns π I L (p L) = π L. π H < π L. If the entrant enters in the second period, both rms compete as duopolists. The incumbent receives pro ts of DH I if their costs are high, and DL I if their costs are low. The entrant receives pro ts of D H if the incumbent has high costs, and DL if the incumbent has low costs. The following relations hold, D I L > D I H > 0 D H > 0 > D L Recall that the entrant only wants to enter if the incumbent has high costs, as denoted by these pro t levels. ric Dunaway (WSU) cons 425 Industrial Organization 21 / 45

22 This is what is known as a signaling game. The entrant starts with some prior belief about the incumbent s costs. The incumbent is able to send a signal to the entrant about their cost level through the price they charge in the rst period. This signal does not have to be truthful. The entrant then updates their beliefs with this new information and decides whether or not to enter the market. ric Dunaway (WSU) cons 425 Industrial Organization 22 / 45

23 I π H + D H, D H µ H p H Incumbent p L µ L I I π H (p L )+ D H, D H 2π H, 0 N θ High Cost N I π H (p L ) + π H, 0 I I π L (p H )+ D L, D L ntrant Nature 1 θ Low Cost ntrant I π L + D L, D L I π L (p H ) + π L, 0 N 1 µ H p H Incumbent p L 1 µ L N 2π L, 0 ric Dunaway (WSU) cons 425 Industrial Organization 23 / 45

24 Unfortunately, backward induction is not feasible for most games of incomplete information. Since the entrant doesn t have all the information, we can t say for certain what their best response will be. In games of incomplete information, we use a technique called forward induction. We work our way through every possible strategy that the incumbent could do, and then determine if that strategy is a perfect Bayesian equilibrium. It s not as scary as it sounds. ric Dunaway (WSU) cons 425 Industrial Organization 24 / 45

25 The incumbent has a total of four possible strategies, and it involves sending a signal upon observing their own costs. 1. If the incumbent has high costs, charge a high price, and if the incumbent has low costs, charge a low price. 2. If the incumbent has high costs, charge a low price, and if the incumbent has low costs, charge a high price. 3. Charge a high price regardless of the incumbent s costs. 4. Charge a low price regardless of the incumbent s costs. ric Dunaway (WSU) cons 425 Industrial Organization 25 / 45

26 We can eliminate two of these strategies right away. When costs are low, it s better for the entrant to not enter the market. An incumbent with low costs has zero incentive to send a signal that their costs are high through a high price. Thus, our two remaining strategies are: 1. If the incumbent has high costs, charge a high price, and if the incumbent has low costs, charge a low price. 4. Charge a low price regardless of the incumbent s costs. Let s look at both of them. ric Dunaway (WSU) cons 425 Industrial Organization 26 / 45

27 If the incumbent has high costs, charge a high price, and if the incumbent has low costs, charge a low price. This corresponds with the incumbent being truthful about their costs to the entrant. This strategy is very useful to the entrant because they can update their beliefs. If they observe a high price, they believe for sure that the incumbent has high costs, i.e., µ H = 1. If they observe a low price, they believe for sure that the incumbent has low costs, i.e., µ L = 0. This e ectively removes the incomplete information. ric Dunaway (WSU) cons 425 Industrial Organization 27 / 45

28 I π H + D H, D H µ H p H Incumbent p L µ L I I π H (p L )+ D H, D H 2π H, 0 N θ High Cost N I π H (p L ) + π H, 0 I I π L (p H )+ D L, D L ntrant Nature 1 θ Low Cost ntrant I π L + D L, D L I π L (p H ) + π L, 0 N 1 µ H p H Incumbent p L 1 µ L N 2π L, 0 ric Dunaway (WSU) cons 425 Industrial Organization 28 / 45

29 Upon observing a high price, the entrant believes with certainty that the incumbent has high costs, so they are sure that they are at the top node. Thus, the compare the payo of DH if they enter the market versus 0 if they do not. Since DH > 0, the entrant s best response is to enter the market. Upon observing a low price, the entrant believes with certainty that the incumbent has low costs, so they are sure that they are at the bottom node. They compare the payo of DL if they enter the market versus 0 if they do not. Since DL < 0, the entrant s best response is to not enter the market. ric Dunaway (WSU) cons 425 Industrial Organization 29 / 45

30 I π H + D H, D H µ H p H Incumbent p L µ L I I π H (p L )+ D H, D H 2π H, 0 N θ High Cost N I π H (p L ) + π H, 0 I I π L (p H )+ D L, D L ntrant Nature 1 θ Low Cost ntrant I π L + D L, D L I π L (p H ) + π L, 0 N 1 µ H p H Incumbent p L 1 µ L N 2π L, 0 ric Dunaway (WSU) cons 425 Industrial Organization 30 / 45

31 Now that forward induction is done, we know that the entrant is satis ed with this strategy combination. However, forward induction has one more step: We need to make sure the incumbent is also satis ed with their own strategy, given the entrant s best responses. We know that if the incumbent has low costs, they ll never want to charge a high price. If they did decide to charge a high price, this would cause the entrant to believe they had high costs and they would enter the market. The incumbent s payo change fall from 2p L to π I L (p H ) + DL I, which is strictly worse for the incumbent. Thus, a low cost incumbent has no incentive to deviate from their given strategy of signalling a low price. ric Dunaway (WSU) cons 425 Industrial Organization 31 / 45

32 What about a high cost incumbent? If they deviated to a low price, this would cause the entrant to believe that they had low costs and they wouldn t enter the market. The incumbent s payo would change from π H + D I H to πi H (p L) + π H. It would be better to deviate and set a low price if π I H (p L) + π H > π H + D I H π I H (p L) > D I H Intuitively, to convince the entrant that they are a low cost rm, the incumbent has to charge a low price and thus earn less pro t. If doing that, plus the pro t they make in the second stage as a monopolist is more than the pro ts they would receive by pricing truthfully then acting as a duopolist in the second stage, then it s better to deviate. This means we have a conditional perfect Bayesian quilibrium. If π I H (p L) DH I, the incumbent will price according to their costs, and the entrant will enter when the price is low and not enter when the price is high. ric Dunaway (WSU) cons 425 Industrial Organization 32 / 45

33 Let s look at the other possible strategy for the incumbent: Charge a low price regardless of their costs. In this case, a low cost incumbent would be signaling truthfully, but a high cost incumbent would be pretending that they have low costs. They do this in hopes that it prevents the entrant from entering the market. When the incumbent signals that they have low prices regardless of their costs, the entrant receives no useful information from that signal. The entrant thus relies on the prior probability that the incumbent has high costs when they form their beliefs, i.e., µ L = θ. ric Dunaway (WSU) cons 425 Industrial Organization 33 / 45

34 I π H + D H, D H µ H p H Incumbent p L µ L I I π H (p L )+ D H, D H 2π H, 0 N θ High Cost N I π H (p L ) + π H, 0 I I π L (p H )+ D L, D L ntrant Nature 1 θ Low Cost ntrant I π L + D L, D L I π L (p H ) + π L, 0 N 1 µ H p H Incumbent p L 1 µ L N 2π L, 0 ric Dunaway (WSU) cons 425 Industrial Organization 34 / 45

35 Since there is uncertainty from the entrant as to which node they are at, they simply choose the action that yields the highest expected payo. If they choose to enter, they receive a payo of DH (a positive number) with probability θ, and a payo of DL (a negative number) with probability 1 θ. If they choose to not enter, they receive a payo of 0 with certainty Thus, the best response for the entrant is to enter if and solving this expression for θ, µ L D H + (1 µ L )D L > 0 µ L = θ > DL DH DL > 0 ric Dunaway (WSU) cons 425 Industrial Organization 35 / 45

36 Intuitively, if the entrant has a high enough belief that the incumbent has high costs (i.e., that they are blu ng), it s better for them to enter the market. We then have two di erent best responses for the entrant depending on the value of θ. We need to analyze both of them. nter if Do not enter if θ > θ DL DH DL DL DH DL Note: If, for some reason, the entrant observes a high price signal from the incumbent, the will enter the market. This is known as the "o the equilibrium path" best response. Normally, we need to do some analysis for this, but we re just going to assume it here. ric Dunaway (WSU) cons 425 Industrial Organization 36 / 45

37 I π H + D H, D H µ H p H Incumbent p L µ L I I π H (p L )+ D H, D H 2π H, 0 N θ High Cost N I π H (p L ) + π H, 0 I I π L (p H )+ D L, D L ntrant Nature 1 θ Low Cost ntrant I π L + D L, D L I π L (p H ) + π L, 0 N 1 µ H p H Incumbent p L 1 µ L N 2π L, 0 ric Dunaway (WSU) cons 425 Industrial Organization 37 / 45

38 In our rst case, we have that θ > DL DH DL and the entrant decides to enter regardless of the signal that they receive from the incumbent. Does the incumbent want to go along with its original strategy in this case? If the incumbent has high costs, they could go along and receive a payo of π I H (p L) + DH I, or they could deviate to charging a high price, knowing that the entrant is going to enter anyways, and receive a payo of π H + DH I. Clearly, deviating is a better strategy for the incumbent. Blu ng about their costs (and lowering their pro ts) just to have the entrant still enter the market is worse o than just being honest. Thus, this cannot be a perfect Bayesian equilibrium. ric Dunaway (WSU) cons 425 Industrial Organization 38 / 45

39 I π H + D H, D H µ H p H Incumbent p L µ L I I π H (p L )+ D H, D H 2π H, 0 N θ High Cost N I π H (p L ) + π H, 0 I I π L (p H )+ D L, D L ntrant Nature 1 θ Low Cost ntrant I π L + D L, D L I π L (p H ) + π L, 0 N 1 µ H p H Incumbent p L 1 µ L N 2π L, 0 ric Dunaway (WSU) cons 425 Industrial Organization 39 / 45

40 In the second case, we have that θ DL DH DL and the entrant decides to not enter the market when they observe a low price. Does the incumbent want to go with this strategy? The low cost incumbent has no objections, 2π L > π I L (p H ) + DL I. The high cost incumbent can go along with it and receive a payo of π I H (p L) + π H, or deviate to charging a high price and receive a payo of π H + DH I. The incumbent will want to deviate if π H + D I H > π I H (p L) + π H D I H > π I H (p L) Just like before, the incumbent only wants to blu if the pro ts they make from blu ng exceed those they would make by just signaling their true costs. ric Dunaway (WSU) cons 425 Industrial Organization 40 / 45

41 Thus, we have a second conditional perfect Bayesian equilibrium, The incumbent charges a low price regardless of its costs, and the entrant enters upon observing a high price and does not enter upon observing a low price if θ DL DH DL and π I H (p L) D I H Combining our two perfect Bayesian equilibria, we can see that the relationship between π I H (p L) and DH I is crucial to the incumbent s behavior. If it s better for the incumbent to not blu, even though it allows entry, then they should not blu. If it s better for the incumbent to blu, and they know the entrant will fall for the blu, then they should blu. ric Dunaway (WSU) cons 425 Industrial Organization 41 / 45

42 Thus, signaling can be an e ective method to deter entry into a market. They key is that it has to be pro table for the rm to blu to the entrant, and the entrant has to fall for the blu. The signaling game model is famous in game theory, and quite applicable to the real world. Why are you even in college? You re trying to send a signal to a potential employer that you have high abilities. ducation is an e ective signal. What kind of signals do you send or look for when playing a relationship game? ric Dunaway (WSU) cons 425 Industrial Organization 42 / 45

43 Summary When we deal with incomplete information, it s possible that a rm with more information that the other can exploit the other rm. This is also true among all kinds of agents. Information is power. Incomplete information and signaling can e ectively deter entry into a market. ric Dunaway (WSU) cons 425 Industrial Organization 43 / 45

44 Next Time Midterm! After that, Contracts and Repeated Games. Reading: , ric Dunaway (WSU) cons 425 Industrial Organization 44 / 45

45 Homework 4-5 Work on that notecard. I ll write an example for this next week in the problem solving session. ric Dunaway (WSU) cons 425 Industrial Organization 45 / 45