Games of strategy dixit 4th edition pdf download

Combining Sequential and Simultaneous Moves 7. Dixit has been the John J. Trivia About Games of Strategy. This outstanding new text by David Kreps, Microeconomics for Managersunderscores the connections between contemporary microeconomics and business, using full-length, gamea case studies to show prospective managers how economic models can yield answers to practical problems.

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Of course we believe this to be the truth of the matter. Each student is to write his or her name on the card, and a number between 0 and The cards will be collected and the numbers on them averaged.

The student whose choice is closest to half of the average is the winner. These rules are, of course, explained in advance and in public. The Nash equilibrium of this game is 0; it results from an iterated dominance argument. Since the average can never exceed , half of the average can never exceed Therefore, any choice above 50 is dominated by Then the average can never exceed 50,.

The first time the game is played, the winner is usually close to This second group chooses much smaller numbers, and the winner is close to 10 as if one more round of the dominance calculation were performed or even 5 or 6 as if two more rounds were performed.

Incidentally, we have found that learning proceeds somewhat faster by watching others play than when the same group of 10 plays successively. Perhaps the brain does a better job of observation and interpretation if the ego is not engaged in playing the game. Again hold a brief discussion. The points to bring out are: 1. The logical concept of dominance, iterated elimination of dominated strategies, and the culmination in a Nash equilibrium.

Getting close to the Nash equilibrium by the experience of playing the game. Whether it is a crucial flaw of the theory that zero is rarely exactly attained or true that the theory gives a good approximation can be a point to be debated depending on the time available. The idea that if you have good reason to believe that others will not be playing their Nash equilibrium strategies, then your optimal choice will also differ from your own Nash equilibrium strategy.

The discussion can also touch on the question of what would happen if the object of the game were to come closest to the average, not half of the average. The game has multiple Nash equilibria, each sustained by its own bootstraps.

Details of this are best postponed to a later point in the course where you cover multiple equilibria more systematically, but a quick mention in the first class provides students with an interesting economic application at the outset. You can also stress the importance of this game in their own lives.

Part or even all of their social security is likely to be in individual. When they decide how to invest this sum, they will have to think through the question: Will the historical pattern of returns and volatility of various assets persist when everyone makes the same decisions that I am now contemplating?

In the context of saving for retirement this can be very costly. In this game, two players, A and B, are chosen. The instructor places a dime on the table. This goes on to the maximum of a dollar five turns each. The players are told these rules in advance. As with the flag game, you can play this game five times in succession with different pairs of players for each game.

Keep a record of where the game stops for each pair. This game is discussed in the text Chapter 3, Figure 3. Our experience is that the simple, theoretical subgameperfect equilibrium of immediate pickup is never observed.

Most games go to 60 or 70 cents, but you do see the students thinking further ahead. Later pairs learn from observing the outcomes of earlier pairs, but the direction of this learning is not always the same. Sometimes they collude better; sometimes they get closer to the subgame-perfect outcome.

After the five pairs have played, hold a brief discussion. Ask students why they made the choices that they did. This game is discussed in the text Chapter 3, Figure 3. Our experience is that the simple, theoretical subgame- perfect equilibrium of immediate pickup is never observed.

Most games go to 60 or 70 cents, but you do see the students thinking further ahead. Later pairs learn from observing the outcomes of earlier pairs, but the direction of this learning is not always the same.

Sometimes they collude better; sometimes they get closer to the subgame-perfect outcome. Ask students why they made the choices that they did. Investigate why they did not achieve the rollback equilibrium. Did the players fail to figure it out, or did they understand it instinctively but have different objective functions?

If you prefer to cover simultaneous-move games first, then you might want to save this game until after you have completed that material. After relating the story, ask each student to pretend that she is one of those taking the exam and must answer the tire question on the card.

Collect the cards and tabulate the answers on the board. Start a discussion about why different students chose different tires; focus on the difficulties of obtaining a focal equilibrium when players have different backgrounds or concerns.

You can also relate the discussion back to the material in the text regarding the necessity of being prepared to face a strategically savvy opponent at any time.

If A refuses, the game is over and neither gets anything. Keep a record of the successive outcomes. Also, consider how the discrepancy changes with the second-round fraction. GAME 6—Divide a Dollar This game asks pairs of students or each student individually, if you use a handout and match students with a random opponent after the fact to divide a dollar between them.

You can play this with real money if you can afford it; we have managed to play this particular game without actual cash with perfectly acceptable results. In actual play this is a game with discrete strategies, for each player, or fewer if the choices are restricted to be multiples of nickels or dimes or even quarters.

Thus, it is also relevant to and discussed again in Chapter 4. But you may prefer to conduct an analysis of the game, treating the choices as continuous variables, in which case the game could be placed in Chapter 5. This game is in direct contrast, then, with the tire game described in Game 4 in which there are also multiple equilibria but none are as obviously focal as 50 cents each is here.

In some cases, there are focal outcomes; in others, players may prefer to alternate among the different equilibria. You can lead from here into the idea of mixed strategies without much difficulty.

Show students a stack of pennies to give them a better idea of what the jar might contain. While the jar is going around, explain the rules. This is also a good way for you to get to remember their names during the first meeting of the class or the section.

The winner will pay his bid and get money paper and silver, not pennies equal to that in the jar. Ties for a positive top bid split both prize and payment equally. When you explain the rules, emphasize that the winner must pay his bid on the spot in cash. After you have collected and sorted the cards, write the whole distribution of bids on the board. Thus, the estimates are on the average conservative.

The emphasis of this game is a concept relating to auctions that are not covered in the text until Chapter It is a simple enough game to play early in the semester if you want to increase interest in the topics or hook additional students. One could certainly save this game until ready to cover auctions. Hand out cards.

Ask each student to write her name and a bid in whole quarters. Collect the cards. All players pay the instructor what they bid, win or lose. Hold a brief discussion about the distribution and the value of the optimal bid.

If that happens, you will have to find ways of returning the profit to the class; we have done this by having a party if the sum is large enough or by bringing cookies to the next meeting if the sum is small. Of course, do not announce this plan in advance. This game is also treated in Chapter If you play the game on the first day, you can lead up to at least some of the points made there, even though the analysis at this early stage cannot go anywhere close to that level.

If you prefer to follow this game with a more in-depth discussion and, perhaps, the derivation of the formula for the optimal bid, then you want to wait and play it when you get to Chapter Movie Excerpts Many movies contain scenes that illustrate some aspect of strategic interaction. Most movies or excerpts from films are best shown later in the course, in conjunction with the particular theoretical ideas being developed.

But one short scene worth showing at the outset, because many of your students will have seen the movie, is the poison scene from The Princess Bride. In it the hero Westley challenges one of the villains Vizzini to a duel of wits. Westley will poison one of two wine cups without Vizzini observing his action and set one in front of each of them. Vizzini will choose a cup for himself; Westley then must drink from the other cup. Vizzini goes through a whole sequence of arguments as to why Westley would or would not choose one cup or the other.

Finally, he believes he knows which cup is safe and drinks from it. You will want to pause the video at this point to have a brief discussion. If Westley thinks through to the same point that leads Vizzini to believe that a particular cup will contain the poison, then he should instead put the poison in the other cup.

Any systematic action can be thought through and defeated by the other player. Therefore, the only correct strategy is to be unsystematic or random.

This is a good way to motivate the idea of mixed strategies. The princess is surprised to find that Westley had put the poison in the cup he placed closer to himself.

So you can get this idea in at the outset of the course and tell the students that it will be discussed in greater depth in Chapter 8.