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Oligopoly • Oligopoly is a market dominated by a relatively small number of large firms • Unconcentrated markets have HH < 1,000 • Products are either standardized or differentiated • Barrier to entry exist • Price, Output and profits depend on actions, reactions, and counteractions
Basic Oligopoly Models • “Sweezy” Oligopoly – A firm assumes that rivals will cut prices when it reduces its price but will not increase prices when it increases the price – result: Price rigidity • “Cournot” Oligopoly – A firm decides its output based on the output of rivals and vice versa – results: firms divide the market • “Betrand” Oligopoly – Firms compete by undercutting each other’s price – result: Price wars and no profits • “Stakelberg” Oligopoly: A firm moves first and commits to an output level before rivals. Rivals decide their output based on the leader’s output – results: staus quo
Cartel Agreement among competing firms to fix prices, output and marketing. Occurs in oligopoly markets Can be explicit or Implicit Legal or illegal
Explicit Cartels • Pure – all firms join the cartel and all have the same costs and costs structure • Perfect – all firms join the cartel but firms have different costs and cost structures • Imperfect – Not all firms join and firms have the same or different costs and cost structures
Implicit Cartels • Firms coordinate strategies without explicit cooperation while recognizing their interdependence. • Firms play strategic games • Firms exploit gray area in anti-trust laws
Dynamics of an Explicit Cartel (Explicit collusion) Initial position: producers behave competitively P=AC (no economic profits) Producers have an agreement to increase the price Producers set quota to control cheating Firms make economic profits As P>MC>AC, each producer has an incentive to produce more than the quota The cartel breaks down as each producer cheats The cartel has to adopt additional strategies to extend the life of the cartel
Some Strategies to facilitate strategic coordination • Hire a cartel enforcer • Centralize or consolidate trade of members and non-members • Control key inputs • Establish specifications and standards • Hire quota enforcers • Divide the market geographically • Limit market shares and set collusion terms other than price • Influence government so that it ‘regulates” industry • Pay for not producing or buy production from others
Case: Government as an Enforcer of coordination • Government imposes tax on producers • Variable cost rise, supply falls, PRP (price received by producers) fall and PPC (price paid by consumers) increase • This is equivalent to a government that figurative buys x for PRP and resells x for PPC
Mafioso Economics • Merchants in a city compete and charge price = Po • "Mafioso Jane" tells merchants that they have to charge P1 (higher than Po) and threatens merchants if they do not obey • Merchants in general make more profits at higher price P1. They pay for a fee or “private tax” to "Mafioso Jane" for services rendered • "Mafioso Jane" acts as a cartel enforcer. • Merchants gain by having "Mafioso Jane" put order in the market and discipline cheaters • "Mafioso Jane" is acting like a government by regulating entry and imposing taxes
Learning Objectives • Define game theory, and explain how it helps to better understand mutually interdependent management decisions • Explain the essential dilemma faced by participants in the game called Prisoners’ Dilemma • Explain the concept of a dominant strategy and its role in understanding how auctions can help improve the price for sellers, while still benefiting buyers
Overview I. Introduction to Game Theory II. Simultaneous-Move, One-Shot Games III. Infinitely Repeated Games IV. Finitely Repeated Games V. Multistage Games
Game Theory • Optimization has two shortcomings when applied to actual business situations • Assumes factors such as reaction of competitors or tastes and preferences of consumers remain constant. • Managers sometimes make decisions when other parties have more information about market conditions. • Game theory is concerned with “how individuals make decisions when they are aware that their actions affect each other and when each individual takes this into account.” • Game Theory is a useful tool for managers
In the analysis of games, the order in which players make decisions is important • Simultaneous-move game- Each player makes decision without knowledge of other players decision • Sequential-move game: player makes a move after observing other player’s move
One shot game – underlying game is played only once • Repeated game – underlying game is played more than once
How managers use game theory: Betrand Duopoly game: 2 gas stations – no location advantage. Consumers view product as perfect substitutes and will purchase from station that sells at lower price. First thing manager must do in the morning is to tell attendant to put up price without knowledge of rival’s price. This is a simultaneous move game. If Manager of station A calls in price higher than B will lose sales that day
Normal Form Game • A Normal Form Game consists of: • Players. • Strategies or feasible actions. • Payoffs.
11,10 10,11 12,12 10,15 10,13 13,14 A Normal Form Game Player 2 12,11 11,12 14,13 Player 1
Simultaneous-move, One shot game • Important to managers making decisions in an environment of interdependence. E.g. profits of firm A depends not only on firm’s A actions but on the actions of rival firm B as well.
-10, 7 10,10 Normal Form Game:Scenario Analysis Player 2 10,20 15,8 Player 1
What’s the optimal strategy? Complex question. Depends on the nature game being played. The game above is easy to characterize the optimal decision– a situation that involves a dominant strategy. A strategy is dominant if it results in the highest payoff regardless of the action of the opponent
For player 1, the dominant strategy is UP. Regardless of what player 2 chooses, if A chooses UP, she’ll earn more. • Principle: Check to see if you have a dominant strategy. If you have one, play it.
What should a player do in the absence of a dominant strategy (e.g. Player 2)? Play a SECURE STRATEGY -- A strategy that guarantees the highest payoff given the worst possible scenario. Find the worse payoff that could arise for each action and choose the action that has the highest of the worse payoffs.
Secure strategy for player 2 is RIGHT. Guarantees a payment of 8 rather than 7 from LEFT 2 shortcomings: • Very conservative strategy • Does not take into account the optimal decision of your rival and thus may prevent you from earning a significantly higher payoff. Player 2 should actually choose LEFT, knowing that player 1 will play UP
Principle: Put yourself in your rival’s shoes If you do not have a dominant strategy, look at the game from your rival’s perspective. If your rival has a dominant strategy, anticipate that she will play it.
11,10 10,11 12,12 10,15 10,13 13,14 Putting Yourself in your Rival’s Shoes • What should player 2 do? • 2 has no dominant strategy! • But 2 should reason that 1 will play “a”. • Therefore 2 should choose “C”. Player 2 12,11 11,12 14,13 Player 1
Player 2 Player 1 11,10 10,11 12,12 10,15 10,13 13,14 The Outcome 12,11 11,12 14,13 • This outcome is called a Nash equilibrium: • “a” is player 1’s best response to “C”. • “C” is player 2’s best response to “a”.
Nash Equilibrium • Given the strategies of other players, no player can improve her payoff by unilaterally changing her own strategy. • Every player is doing the best she can given what other players are doing. • In original example, Nash equilibrium is when A chooses UP and B chooses LEFT.
Application of One shot games • Two managers want to maximize market share. • Strategies are pricing decisions. (charge high or low prices) • Simultaneous moves. • One-shot game. (firms meet once and only once in the market)
The Market-Share Game in Normal Form Manager 2 Manager 1
Market Share game Equilibrium • Each manager’s best decision is to charge a low price regardless of the other’s decision. Outcome of game is that both firms charge a low price and earn 0 profits • Low prices for both managers is the Nash Equilibrium
If firms collude to charge high prices, profits will be higher for both • Classic case in Economics called dilemma because the Nash equilibrium outcome is inferior (from the firms viewpoint) to the situation where they both “agree” to charge high prices Even if firms meet secretly to collude, is there an incentive to “cheat” on the agreement?
To advertise or Not? • Your firm competes against another firm for customers • You and your rivals know your product will be obsolete at the end of the year (one shot game) and must simultaneously determine whether or not to advertise. • In your industry, advertising does not increase industry demand but induces consumers to switch among the products of the different firms
An Advertising Game Manager 2 Manager 1
To advertise or Not? • Dominant strategy of each firm is to advertise. unique Nash equilibrium. • Collusion will not work because this is a one-shot game and if there’s agreement not to advertise, each firm will have an incentve to cheat.
Key Insight: • Game theory can be used to analyze situations where “payoffs” are non monetary! • We will, without loss of generality, focus on environments where businesses want to maximize profits. • Hence, payoffs are measured in monetary units.
Examples of Coordination Games • Industry standards • size of floppy disks. • size of CDs. • National standards • electric current. • traffic laws.
Coordination Decisions: Firms don’t have competing objectives but coordinating their decisions will lead to higher profits e.g. Producing appliances that require either 90-volt or 120-volt outlets
A Coordination Game in Normal Form Firm B Firm A
Coordination Game: 2 Nash Equilibria • What would you do if you manage Firm A? If you do not know what firm B is going to do, you’ll have to guess what B will do. Effectively, both you and firm B will do better by coordinating your actions. 2 Nash equilibria. If the firms can ‘talk’ to each other, they can agree on what to produce. Notice, there’s no incentive to cheat here This is a game of coordination rather than game of conflicting interest
Simultaneous-Move Bargaining • Management and a union are negotiating a wage increase. • Strategies are wage offers & wage demands. • Players have one chance to reach an agreement and offer is made simultaneously. • Parties are bargaining over how much of $100 in surplus must go to the union
Assume the surplus can be split only into $50 increments • One shot to reach agreement • Parties simultaneously write the amount they desire on a piece of paper. • If the sum of the amounts does not exceed $100, players get the specified amount • If sum exceeds $100, stalemate, costing each player $1
The Bargaining Game in Normal Form Union Management
Simultaneous-Move Bargaining • 3 Nash equilibria outcomes. • Multiplicity of equilbria leads to inefficiency if parties fail to “co-odinate” on an equilibrium • 6 of 9 outcomes are inefficient because they don’t sum up to 100 • Clearly, in this game management must ask for 50 if they
Key Insights: • Not all games are games of conflict. • Communication can help solve coordination problems. • Sequential moves can help solve coordination problems.
Infinitely Repeated Games • Game played over and over again. Players receive payoff during each repetition of game • Firms compete week after week, year after year game is repeated over time • To evaluate profits earned during this game, consider the PV of all payoffs. • If payoffs are the same in each period, then for an infinitely played game • PV = 1/i * constant profit
An Advertising Game • Two firms (Kellogg’s & General Mills) managers want to maximize profits. • Strategies consist of pricing actions. • Simultaneous moves. • Repeated interaction.
Equilibrium to the One-Shot Pricing Game General Mills Kellogg’s
When firms repeatedly face this type of matrix, they use “trigger strategy” • Trigger Strategy – is a strategy that is contingent on the past plays of players in a game • A player who adopts a trigger strategy continues to choose the same action until some other player takes an action that “triggers” a different action by the first player
Can collusion work if firms play the game each year, forever? • Consider the following “trigger strategy” by each firm: • “We will each charge the high price, provided neither of us has ever “cheated” in the past. If one of us cheats and charges a low price, the other player will “punish” the deviator by charging low price in ever period thereafter” • In effect, each firm agrees to “cooperate” so long as the rival hasn’t “cheated” in the past. “Cheating” triggers punishment in all future periods.