sequential+move+games


 * __Sequential-Move Games__**

//–noun//
 * game theory**
 * a mathematical theory that deals with strategies for maximizing gains and minimizing losses within prescribed constraints, as the rules of a card game: widely applied in the solution of various decision-making problems, as those of military strategy and business policy. ||
 * Dictionary.com

Some Basic Assumptions:**
 * Everyone fully understands the rules of the game
 * Everyone acts rationally
 * Everyone wants to maximize their outcome


 * Sequential-Move Games** are defined as games where one player makes a move after observing the other player's move. Chess, tic-tac-toe, and checkers are examples of sequential-move games. An important feature to sequential-move games is that the second-mover has information about how the first-mover is going to play. However, this does not always give the advantage to the second-mover because the first-mover is also aware that he is giving information to the second-mover. The first-mover may make a decision to steer the second-mover in the direction that best fits the short-term and long-term goals of the first mover. The second-mover also knows that first-mover may misrepresent its position with its decision and can react accordingly.

Avinash Dixit and Barry Nalebuff's paper about Game Theory points out that "a general principle for a player in a sequential-move game is to look ahead and reason back. Each player should figure out how the other players will respond to his current move, how he will respond in turn, and so on. The player anticipates where his initial decisions will ultimately lead, and uses this information to calculate his current best choice." Three examples of sequential-move games are:


 * The Entry Game**- where a company must decide wether or not to enter a market depending on how firms already in the market will react. A key to this game is to figure out how to decipher threats that might be made to keep a firm from entering. If for instance, the threatening firm does not have a sensible incentive to go through with the threat then the threat is is not credible and the firm should enter.


 * Innovation**- this game has to do with wether to introduce a new product into a market where it can be cloned by a rival. Many factors weigh into this decision: Are patents available for the product to keep the rival from cloning? Does it matter if the rival clones the new product? Would you believe you rival if he promised not to clone it? All of these questions must be answered to come up with the best decsion.


 * Sequential Bargaining**- This game involves understanding the opportunity cost of rejecting or accepting an offer. Let say for instance you have can offer $100 as a settlement or $1 as a settlement and the firm can either accept or reject the offer. If they accept they get the offer if they reject they get nothing. Now lets say that the firm threatens to reject the settlement if you do not offer $100. You should offer $1 because they will obviously accept it because if they do not they will get nothing. This is called a subgame perfect equilibrium.

A **subgame perfect equilibrium** is a condition describing a set of stategies that constitute a Nash equilibrium and allows no player to improve his own payoff atg any stage of the by changing strategy.

A good way to understand how a sequential move game works is to use an extensive-form game. //According to Managerial Economics and Business Stategy; 5th Edition// an **extensive-form game** "summarizes the player, the information available to them at each stage, the stratagies available to them, the sequence moves, and the payoffs resulting from alternative statagies."

The followingare examples of extensive-form games:

The following is an example to understand how this form works:

In the above example there are two players. Player 1 can choose Up (U) or Down (D). After Player 1 chooses, Player 2 can either choose U or D dependent on what Player 2 chose. The end numbers are the related outcomes to the final decision given in form Player 1, Player 2.

Example: Player 1 chooses U, Player 2 also chooses U, therfore the end result is both get 0. However, If Player 1 chose U, presumably Player 2 would choose D because it would maximize his result even though Player 1 would get more. Knowing this information and working backwards would allow Player 1 to maximize their end result because they are able to see the end result. Player 1 would choose U in this example becuase it maxmizes their outcome presuming Player 2 was working for their own best interest.

It is important to note that sequential-move games can only happen if every player (perfect information) or some of the players (imperfect information) observe the previous moves of other players. If no players observe previous moves then it is a simultanious-move game. In an imperfect information game some players are using a sequenetial-move game and some are using a simultaneous-move game.

The above extensive form game depicts a situation with imperfect information where Player 1 selects either U or D, but Player 2 has no idea what Player 1 chose. Player 1 wants Player 2 to believe that they chose U when they actually chose D because it would result in a payoff of 3 rather than 2. However, because Player 2 is aware that Player 1 knows that Player 2 doesn't know what they chose, Player 2 supposes that Player 1 would choose D because of the possibilty that by choosing U they could possibly get nothing. A situation where a Nash Equilibrium results in this type of reaction is called a perfect Bayesian equilibrium where "every strategy is rational given the beliefs held and every belief is consistent with the strategies played (Wikipedia)."


 * Centipede Game**

In the centipede game Player 1 can eith choose to take a pot (4,1) or pass to Player 2. Player 2 can then choose to do the same until a termination stage. Player 1 knows that with each pass he can increase his earnings at each choice point. However, using backward induction Player 1 should choose the to take the pot on the very first turn. Because, knowing the end result, Player 2 would take the pot on his last try for maximum benefit before termination (8,32). Knowing that Player 2 will act in this way Player 1 would select at (16,4) and so on until it becomes clear that Player 1's best option is to pick on the first try. Without using backward induction, it has been shown that many players will not act rationally and will continue to pass because of their hope for higher returns.

Sequential-games can be thought of in terms of a Chess game. Player 1 makes the first move and Player 2 makes a move having perfect information in order to obtain maximum benefit. However, like in most Chess games a winner is determined after a series of decisions. Sometimes the first-mover wins, sometimes the second-mover wins. This could be because of different strategies employed during the game, experience level, the abilty to read someones intentions, catching someone off guard, making mistakes, tricking them, anticipation of moves, or any number of different variables. Sequential-move games are common in business strategy, but are not always as clear-cut as the examples in this explaination. Adding another player can complicate and multiply the decision process exponentially. It is also important to remember that people may not act rationally or with complete information as the models above showed.

1. What are the basic assumption one has to make when discussing sequential-move games? A. Everyone fully understand the rules B. Everyone acts rationally C. Everyone must know have full diclosure of all of the previous decisions D. Everyone acts wants to maximize their outcome E. Four of the above F. Three of the above
 * Questions**

Use the follwing diagram for the next three questions:

2. If Player 1 chooses D Players 2's best option is to: A. Choose U' B. Choose D' C. Choose nothing

3. If Player 1 and Player 2 switched postions on the diagram (Player 2 starts where Player 1 started), but still kept the same results (P1,P2) which decision would best for Player 2? A. Choose U B. Choose D C. It doesn't matter D. Choose nothing

4. True or False: The first person to act has an advantage over the sencond person to act. A. True B. False

5. Which of the following are exaples of sequential-move games: A. Bingo B. Chess C. Centipede Game D. Roulette E. Tic-Tac-Toe

1. F. Only and at least one person must have full information in order for it to be a sequential-move game 2. A. U' is the best possible result given Player 1's choice. However, Player 1 would not be likely to chooose D because it does not allow Player 1 to maximize their benefit. 3. A. Either way Player 2 would likely get the same benefit from both options, however Player 1's benefit would be less if Player 2 chooses U. 4.False. Depending on the a given a industry it may be beneficial to allow a First-mover to spend on educating the public about a product and incuring R&D costs. Then the second-mover can use its resources more effectively toward an already existent market. 5. B,C,and E are example of sequential-move games. Both Bingo and Roulette involve making decisions on unpredictable outcomes.
 * Answers**


 * References

Dictionary.com http://www.econlib.org/library/Enc/GameTheory.html http://en.wikipedia.org/wiki/Perfect_Bayesian_equilibrium#Perfect_Bayesian_Equilibrium http://en.wikipedia.org/wiki/Centipede_game http://www.ams.org/featurecolumn/archive/rationality.html**