Game theory of cheating firms발음듣기
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Game theory of cheating firms
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[Male Voice] In the last video we saw how there could be an industry that has two firms, a duopoly, and if those two firms coordinate they could behave as a monopolist and they could optimize their collective economic profit.발음듣기
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In the last video we saw that would happen when they produced 50 units per period, and they could split it, assuming these were two identical firms, by each producing half of it.발음듣기
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Then we saw that there was an incentive to cheat; that by producing extra units, from a market's point of view, the marginal economic, or the economic profit on those incremental units would be negative,발음듣기
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so the whole economic profit would shrink a little bit as you produced units beyond that, but the cheater would get a bigger chunk of those units, or the bigger chunk of that economic profit.발음듣기
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The cheater could actually gain, go from $250 per time period to $280, and it would be all at the expense of the non-cheater, and then some, who would lose even more than what the cheater gained.발음듣기
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Obviously who was initially the non-cheater has an incentive now to cheat, and they'll both keep increasing, they'll both keep increasing production so that if they wanted to keep doing this one-upmanship.발음듣기
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They both have the incentive to keep going assuming that they don't hold to their cartel agreement until you get to a quantity where there's no economic profit left.발음듣기
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Right over here, the way I've drawn it, the demand curve intersects the average total cost curve right over here, and there's no economic profit left.발음듣기
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But at this point, the market price is equal to the average total cost, and so there's no economic profit per unit on average.발음듣기
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All it means is that's the state where there's no other state where you can make someone better off without making the other person worse off.발음듣기
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Now, what I want to think about is how these characters will change their state due to their incentives.발음듣기
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This is where they produce 25, and let's say on the ultimate cheating quantity of 75, and this is somewhat close to the market, or that is the equilibrium quantity if this was perfect competition, they produce half of that, so this is them producing 37.5 units.발음듣기
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This is they've maximized the total economic profit here. There's no other state that one person would benefit without making the other worse.발음듣기
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Now, let's think about whether this is a Nash equilibrium. Let's remind ourselves what Nash equilibrium was.발음듣기
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This was a state where holding all the other players constant, so in this case there's only one other player, a player can't gain by changing strategy.발음듣기
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In this case, changing strategy is changing your output. Let's see if that is true of this state right over here. Well, let's hold A constant.발음듣기
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Is there something B can do, is there change or strategy B can do, that would allow B to gain?발음듣기
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Now B's economic profit is 280, A's is 200. The pie has shrunk, but B has got a larger chunk of it.발음듣기
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There is, holding all others constant, there is a player that can gain by changing their strategy.발음듣기
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The Nash equilibrium definition, just to make sure, they say it's a state where holding others constant no player can gain by changing strategy.발음듣기
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We just showed that at least one player can gain by changing strategy holding others constant.발음듣기
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If we held B constant at 25, A could gain by changing his strategy, could go right over there.발음듣기
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Then regardless of what state we go to, if we go to this state, it's still not a Nash Equilibrium. If we hold A constant, B could improve by increasing his production; or if we hold B constant, then A can still improve by cheating even more.발음듣기
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From any one of these states, if you hold A constant, B could produce more; or if you hold B constant, A could produce more and get some gain.발음듣기
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Then maybe A cheats some more, then B cheats some more, then A cheats a little bit more, B cheats a little bit more, maybe a little bit more past that, then A cheats a little bit more.발음듣기
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The whole time the whole economic profit pie, which is the sum of A and B, is getting smaller and smaller until finally A finally cheats and they're at zero economic profit.발음듣기
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Now let's think about whether this is a Nash equilibrium. Clearly, they won't want to move backwards.발음듣기
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Holding A constant, if B were to produce more than 37.5 from this state right over here, then the total pie will get negative and it doesn't matter if B's getting a larger or smaller chunk of that pie.발음듣기
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If they increase quantity beyond this market quantity of 75, 37.5 each, if we go beyond that, the price that they would be selling at, at that quantity over there, is lower than the average total cost.발음듣기
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You're going to be, the total economic, the average economic profit per unit is going to be negative.발음듣기
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All of a sudden in this topless state, holding others constant; if you hold A constant, B can't gain by changing his strategy, and if you hold B constant A can't gain by changing his strategy, so we are, up here, in a Nash equilibrium.발음듣기
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The optimal state was here, but because they both wanted to cheat, they both wanted to do this one-upmanship, they both broke their contracts, they could end up in this state over here.발음듣기
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What they could do, and this is not what Nash applies to, they could say okay, we've been really ruining each others' business.발음듣기
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That is not, and they could maybe try to go back to this state, and that does not mean that this is not a Nash equilibrium because by coordinating again we're not holding the others constant.발음듣기
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