Welcome back. In this session,

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

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

the concepts of iterative dominance, and commitment.

Now, we saw if one party or both,

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

if one or both have a dominant strategy,

we'll end up with a Nash equilibrium.

And if both have a dominant strategy equilibrium,

we'll end up with the dominant strategy equilibrium,

even more exclusive form of Nash equilibrium.

What if neither party has a dominant strategy?

Could we still end up with a Nash equilibrium?

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

Let's start with table 15.1,

two sellers of particular electronic products,

Wal-Mart and Best Buy.

And each of the two sellers has three possible strategies,

high price, medium price, low price.

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

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

and we knew for sure,

Best Buy was going to charge a high price.

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

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

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

So it looks like a potential dominant strategy.

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

Best Buy potentially can choose a low price.

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

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

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

If you reverse the situation,

now we look at Best Buy.

What if Wal-Mart charges a high price?

In this case, Best Buys best option is 105.

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

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

the payoff matrix would be 50 and again,

would be a medium price.

The fly in the ointment again occurs in

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

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

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

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

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

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

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

How can we do this?

Now notice that for Wal-Mart,

its payoff's associated with low price strategy are in

every possible scenario superseded by a medium price strategy.

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

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

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

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

and trido, if Best Buy chose low price.

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

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

Convinced yourself the same is true for Best Buy.

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

No matter what Wal-Mart does.

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

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

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

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

each firm has a dominant strategy.

Wal-Mart is best off going medium price.

Its payoff is higher regardless of what Best Buy does.

If Best Buy had chosen high price,

Wal-Mart's better off 105 versus 90.

If Best Buy goes medium price,

Wal-Mart's again better off going medium.

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

Same is true for Best Buy.

If you knew Walmart was going high,

Best Buy is better off going with medium price strategy.

And if you knew Walmart was going medium,

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

So, Best Buy also has a dominant strategy.

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

Both firms earning $50,

both firms choosing a medium price.

Regardless of what the other party does,

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

Now notice one thing,

and this again a prisoner's dilemma.

Both parties will end up with payoffs that

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

Now as we saw last week,

prisoner's dilemmas are hard to unravel,

unless it's a repeated game setting.

We'll show now through another device commitment,

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

Often in these type of markets,

we'll see a firm say,

"we will not be undersold."

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

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

actually end up resolving the prisoner's dilemma,

and actually end up screwing consumers to the benefit of

the firms operating in this market?

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

What it means is that,

if it chooses a high price,

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

So by asserting, "we will not be undersold,

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

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

"we won't be undersold."

If Wal-Mart's going medium,

Best Buy would never choose a high price strategy.

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

Now if we take those two rectangles off,

notice what we're left with.

Both firms have said we won't be undersold.

So their choice comes down to either or both choosing

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

Their willingness to commit toward not

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

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

And notice, what these firms have done cleverly,

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

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

$25 or $50 per unit,

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

help ensure that they end up with

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

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

we're actually witnessing at times firms seeking

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

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

when Cortes, the Spanish conquistador landed in Latin America.

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

By effectively limiting the number of choices before them,

it helped Cortes in very unfortunate outcome for the natives,

but it helped Cortes's soldiers fight

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

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

gives them a mechanism to end up with

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