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Welcome back. In this session,

Â we'll do one last application of imperfect competition of monopoly theory,

Â and we'll turn in particular to some more nuances dealing with game theory,

Â the concepts of iterative dominance, and commitment.

Â Now, we saw if one party or both,

Â in a simple two party setting of one player or two player,

Â if one or both have a dominant strategy,

Â we'll end up with a Nash equilibrium.

Â And if both have a dominant strategy equilibrium,

Â we'll end up with the dominant strategy equilibrium,

Â even more exclusive form of Nash equilibrium.

Â What if neither party has a dominant strategy?

Â Could we still end up with a Nash equilibrium?

Â It turns out the answer is yes and we'll see why.

Â Let's start with table 15.1,

Â two sellers of particular electronic products,

Â Wal-Mart and Best Buy.

Â And each of the two sellers has three possible strategies,

Â high price, medium price, low price.

Â Now what you can see is that neither of these two parties has a dominant strategy.

Â Why? Let's say, we look at Wal-Mart first,

Â and we knew for sure,

Â Best Buy was going to charge a high price.

Â In this case, the payoff to Wal-Mart would be maximized with the medium price.

Â If Best Buy we knew was going to charge medium price,

Â again, Wal-Mart would be best off charging a medium price again.

Â So it looks like a potential dominant strategy.

Â But the fly in the ointment occurs with the last column,

Â Best Buy potentially can choose a low price.

Â In that case, Wal-Mart's best option,

Â it's the lower triangle in each pay off square of this matrix is a high price.

Â So Wal-Mart doesn't have a dominant strategy.

Â If you reverse the situation,

Â now we look at Best Buy.

Â What if Wal-Mart charges a high price?

Â In this case, Best Buys best option is 105.

Â If Wal-Mart we knew was going to charge a medium price,

Â Best Buy it's the top triangle of each rectangle in

Â the payoff matrix would be 50 and again,

Â would be a medium price.

Â The fly in the ointment again occurs in

Â this symmetric case with Wal-Mart charging a low price.

Â In this case, Best Buy would be best off choosing a high price.

Â So neither Best Buy nor Wal-Mart has a dominance strategy.

Â Why might we still end up in this case with a Nash equilibrium?

Â This's where the concept of iterated dominance comes in.

Â Where we can rule out certain options by players involved in a game

Â theoretic setting that allows us to simplify and move toward an equilibrium.

Â How can we do this?

Â Now notice that for Wal-Mart,

Â its payoff's associated with low price strategy are in

Â every possible scenario superseded by a medium price strategy.

Â So, if we knew Best Buy was going to charge a high price,

Â Wal-Mart would be better off choosing a medium price strategy versus a low price.

Â Ditto if we knew Best Buy was choosing a medium price,

Â Wal-Mart's comparison would be 50-40,

Â and trido, if Best Buy chose low price.

Â So, this low price strategy can effectively be ruled out,

Â can be iterated out of Wal-Mart's portfolio of possible strategies.

Â Convinced yourself the same is true for Best Buy.

Â Its payoffs are always higher choosing medium price versus a low price.

Â No matter what Wal-Mart does.

Â So, by iteration we can also eliminate the low price strategy for Best Buy.

Â So if we knock out the low price option for both these two players,

Â what we end up with is a two by two and a Nash equilibrium that emerges.

Â Why? Because in this two by two reduce setting where we've iterated out two options,

Â each firm has a dominant strategy.

Â Wal-Mart is best off going medium price.

Â Its payoff is higher regardless of what Best Buy does.

Â If Best Buy had chosen high price,

Â Wal-Mart's better off 105 versus 90.

Â If Best Buy goes medium price,

Â Wal-Mart's again better off going medium.

Â So, Best Buy has a dominant strategy of medium price.

Â Same is true for Best Buy.

Â If you knew Walmart was going high,

Â Best Buy is better off going with medium price strategy.

Â And if you knew Walmart was going medium,

Â your payoffs as Best Buy are higher with a medium price strategy 50 versus 44.

Â So, Best Buy also has a dominant strategy.

Â And what we'll end up with is a dominant strategy equilibrium.

Â Both firms earning $50,

Â both firms choosing a medium price.

Â Regardless of what the other party does,

Â this iterative dominance approach has allowed us to achieve a Nash equilibrium.

Â Now notice one thing,

Â and this again a prisoner's dilemma.

Â Both parties will end up with payoffs that

Â are lower than had they both opted for a high price strategy.

Â Now as we saw last week,

Â prisoner's dilemmas are hard to unravel,

Â unless it's a repeated game setting.

Â We'll show now through another device commitment,

Â how we can get out of a prisoner's dilemma.

Â Often in these type of markets,

Â we'll see a firm say,

Â "we will not be undersold."

Â So if you see a lower price at a rival firm, we'll match it.

Â Now, how might such a statement not be undercut, seemingly pro-competitive,

Â actually end up resolving the prisoner's dilemma,

Â and actually end up screwing consumers to the benefit of

Â the firms operating in this market?

Â If Wal-Mart says, "we won't be undersold."

Â What it means is that,

Â if it chooses a high price,

Â it will never want an outcome where Best Buy is choosing a price below a medium price.

Â So by asserting, "we will not be undersold,

Â " Wal-Mart effectively takes this rectangle out of the payoff matrix.

Â Similarly, by Best Buy saying if they also are certain,

Â "we won't be undersold."

Â If Wal-Mart's going medium,

Â Best Buy would never choose a high price strategy.

Â So it takes off that rectangle out of the payoff matrix.

Â Now if we take those two rectangles off,

Â notice what we're left with.

Â Both firms have said we won't be undersold.

Â So their choice comes down to either or both choosing

Â a high price strategy or both choosing a medium price strategy.

Â Their willingness to commit toward not

Â being undersold has allowed them a way out of the prisoner's dilemma.

Â They will be better off both adhering to a high price strategy.

Â And notice, what these firms have done cleverly,

Â and sometimes you'll see firms saying we'll even reward customers to

Â come in with a lower priced product from a competitor with a bonus,

Â $25 or $50 per unit,

Â they're effectively enlisting consumers to help police their actions to

Â help ensure that they end up with

Â a high price outcome to the detriment of consumers that are acting as their police.

Â So in a paradoxical ways when we see claims of we won't be undersold,

Â we're actually witnessing at times firms seeking

Â a higher price outcome at the expense of consumers and to the benefit of firms profits.

Â One last application of commitment devices comes from the 1500s,

Â when Cortes, the Spanish conquistador landed in Latin America.

Â He burned his ships. He burned his ability of his soldiers to get back to Spain.

Â By effectively limiting the number of choices before them,

Â it helped Cortes in very unfortunate outcome for the natives,

Â but it helped Cortes's soldiers fight

Â more ferociously knowing that they didn't have an exit strategy.

Â So in a similar way the commitment device that we saw Wal-Mart and Best Buy,

Â gives them a mechanism to end up with

Â a better outcome as far as these two firms are concerned.

Â