Strategic Thinking:

Chapter Summary:

In strategic conditions, when the parties move concurrently, there are a number of helpful principles to follow: Avoid employing dominated strategies, focus on Nash equilibrium strategies, and consider randomizing. Whenever the parties move sequentially, a strategy must be worked out by looking forward to the final nodes and reasoning back to the original node.

Through unconditional or conditional strategic moves, it might be possible to affect the beliefs or actions of other parties. In several settings, the first mover has the benefit; in others, the primary mover has drawback. Finally, it is significant to consider whether the condition will be played merely once or repeated. The range of probable strategies is broader in a repeated condition.

In a zero-sum game, one party can become enhanced off only when the other is made worse off. In a positive-sum game, one party can become better off devoid of the other being made worse off.

Key Concepts:

General Chapter Objectives:

A) Appreciate how game theory can guide strategic thinking in a broad range of conditions.

B) Describe how the concept of Nash equilibrium forecasts the outcome of strategic conditions where parties act concurrently.

C) Apply the concept of Nash equilibrium to the cartel.

D) Appreciate the utilization of randomized strategies, and compute the Nash equilibrium in the randomized strategies.

E) Differentiate strategic conditions of coordination and competition.

F) Analyze strategic conditions where parties act in sequence by backward induction.

G) Appreciate the utilization of strategic moves to affect the beliefs or actions of other parties.

H) Describe why conditional strategic moves are more cost-efficient than unconditional strategic moves.

I) Understand how repetition enlarges the space of strategies and set of equilibrium.
 
Notes:

1) Strategic thinking:

a) The strategy is a plan for action in a condition where parties actively consider the interactions with one other in making decisions.

b) Game theory is a set of principles and ideas which guides strategic thinking.

c) The principles and ideas of game theory offer an efficient guide to strategic decision making in many conditions.
 
2) Nash equilibrium: for strategic conditions where different parties move concurrently.

a) A game in strategic form: symbolizes a strategic condition where parties act concurrently, exhibiting one party’s strategies all along the rows, the other party’s strategies all along the columns, and the effects for the parties in corresponding cells. This is a helpful way to arrange thinking regarding strategic decisions.

i) A dominated strategy is one which generates worse effects than the other strategy, despite of the selections of the other parties. This makes no sense to adopt a dominated strategy.

ii) Problem of infinite regress: Party’s best decision based on how it predicts the other party to act, that in turn based on how the first party predicts the second party to act, and so forth.

b) Nash equilibrium in a game in strategic form: It is a set of strategies such that, given that the other players select their Nash equilibrium strategies, each and every party prefers its own Nash equilibrium strategy.

i) A stable condition: Usually, when one party adopts Nash equilibrium strategy, the other parties can’t benefit from knowing the strategy.

ii) Gives a logical consistent solution to the trouble of infinite regress.

iii) The Nash equilibrium strategies give a focal point for strategic decision making.

iv) Resolving for the Nash equilibrium or equilibria.

• The formal manner (that is, rule out dominated strategies first and then check each and every residual strategy, one at a time); or
• The informal “arrow” method.

A strategy is dominated when the column or row corresponding to the strategy consists of all arrows pointing out.
When there is a cell with all arrows leading in, then the strategies forming that cell are Nash equilibrium.

c) Non-equilibrium strategies:

i) When one party doesn’t adopt its Nash equilibrium strategy, then the best strategy for the other party might differ or might not differ (example: where all other strategies are dominated) from the Nash equilibrium.

ii) In several games in strategic form, there might be no Nash equilibrium in pure strategies.
 
3) Randomized strategies:

a) A pure strategy: one which does not include randomization.

b) A randomized strategy: It is a strategy for selecting among the alternative pure strategies in accordance with given probabilities. The different probabilities add up to 1.

i) In some conditions, there might be no Nash equilibrium in pure strategies.

ii) The benefit of randomization is to be random. When a party selects in a conscious manner, the other party might be capable to guess or learn the first party’s decision and act accordingly.

c) Nash equilibrium in randomized strategies:

i) A stable situation: Usually, whenever one party adopts Nash equilibrium strategy, the other parties can’t benefit from the learning strategy.

ii) Resolving for Nash equilibrium in the randomized strategies.

• Crossing point of lines symbolizing the outcomes of alternative strategies as the function of probability which the other party’s strategies; or
• Algebra.

4) Competition or coordination:

a) Competitive situation:

i) A zero-sum game is a strategic condition where one party can be better off simply if the other is made worse off (that is, extreme of competition). There is no way for all the parties to become better off.

ii) Condition is zero-sum whenever the effects for the different parties add up to 0 or similar number in every cell of game in the strategic form.

b) Coordination situation:

i) A positive-sum game is the strategic condition where one party can become better off devoid of another being made poorer off.

ii) A network consequence occurs whenever a benefit or cost based on the total number of other users. Different situations of network consequences symbolize positive-sum games.

iii) Nash equilibria are focal points for the strategic thinking. In conditions of coordination, as the necessary issue is coordination among the parties and Nash equilibrium strategies are self reinforcing, it is logical that they meet and employ Nash equilibrium as a basis for discussion.

C) Coopetition:

i) A strategic condition which includes elements of both coordination and competition.

ii) A cartel’s dilemma. In seller cartel, the Nash equilibrium is for all to generate more than their quota: when cartel participants cooperate, they can raise their profit. Though, following the quota is a dominated strategy. Whenever each acts independently, it will decide to surpass its quota-resulting in production at the competitive instead of a monopoly level.

• The seller’s cartel is an illustration of the prisoner’s dilemma.  In prisoner’s dilemma, the Nash equilibrium is for both suspects to admit: even however they would both be better off when they did not confess.
• Cooperation might occur when coopetition is repeated. By conditioning their actions on either exterior events or the prior actions of the other party, the parties might be able to avoid the unwanted outcomes of one shot conditions.

5) Sequencing: situations where different parties move sequentially, instead of simultaneously.

a) Game in extensive form: Symbolizes a strategic situation where parties act in series, showing the series of moves and corresponding outcomes. It comprises of nodes and branches: the nodes are where a party should select an action, and the branches leading from a node symbolize the possible selections.

b) Equilibrium strategy in a game in extensive form: a series of best actions, where each action is decided at corresponding node.

i) Backward induction is the process of looking forward to the final nodes and then reasoning backward in the direction of initial node.

ii) It is distinct from Nash equilibrium strategy, in a game in strategic form where parties move concurrently.
 
6) Strategic Moves:

a) An unconditional strategic move is an action which affects the beliefs or actions of other parties in a favorable manner

i) Usually includes self imposed restrictions and real costs; example: destroying the lithograph plates.
ii) Significance of credibility, example: sunk costs commitments.
iii) Apply an extensive form to examine the impact of a strategic move.

b) First mover benefit gives the party which moves first a benefit over other parties which move later.

i) Not all conditions include first mover benefit; in some conditions, the party which moves later gains a benefit.
ii) Apply an extensive form to recognize conditions including first mover benefit.

c) A conditional strategic move is an action beneath specified conditions to persuade the beliefs or actions of other parties in a favorable manner.

i) Conditional strategic moves are more cost-efficient than unconditional strategic moves.
ii) A threat imposes costs beneath specified conditions; example: poison pill.
iii) A promise conveys advantages beneath specified conditions, example: deposit insurance.
iv) Apply an extensive form to examine threats and promises.
 
7) Repetition:

a) With repeated interaction, a party might condition actions on exterior events or the actions of other parties.

b) The expanded set of strategies might give mount better Nash equilibrium outcomes than in once-only conditions.

c) Tit-for-tat is an equilibrium strategy in the repeated cartel.

i) Whenever competing sellers interact over an extended time period, it is probable to maintain a cartel and attain profit above the competitive level.
ii) A seller conditions its production on the actions of other party at a previous time.  The seller starts by following its quota and will continue till the others surpass their quotas.
iii) Combines a promise (that is, to abide by quota when the others do) with a threat (that is, to generate more than the quota when the others surpass their quotas).
iv) In a cartel which extends to some markets, tit for tat promises greater benefit (that is, increased gain in all the markets where production is limited) and threatens bigger punishment (decreased profit in all the markets covered).

Question-Answer:

A general issue among couples is what to do on the weekend. A woman might wish to go shopping, whereas the man would instead attend a football match. Other things equivalent, both would instead be altogether. Therefore the consequences if the two persons attend separate activities are moderately poor. The game theorists call this the battle of sexes.

a) Make the following game in strategic form. Exhibit the man's strategies all along the left-hand side of the strategic form, and the woman's strategies all along the top of the strategic form. Compute the effects for the man and the woman from each pair of strategies.

b) Recognize the equilibrium or equilibria.

c) How might the equilibrium or equilibria modify if the woman could move first?
 
Answer:

a) To build the game in strategic form, consider the following. When both man and woman spend time altogether either shopping or watching football, they both are in benefit. The man would prefer both watching football, whereas the woman would prefer both shopping. On the other hand, when the man watches football alone whereas the woman shops alone, each will derive few benefit however less than from doing the activity together. The worst situation is where the man shops alone and the woman watch football alone.

In each and every cell, the first number is the man’s advantage and the second number is the woman’s advantage.

b) There are two Nash equilibria: in one, both watch football, whereas in the other, both go shopping. (That is, there is a third Nash equilibrium, in randomized strategies.)

c) In a condition where the woman moves first, there is just one equilibrium. The woman has first mover benefit. When she decides to go shopping, the man should select between football by himself, which gives a benefit of 1, or shopping with woman, which gives a benefit of 2.  He will select shopping.

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