A2 Economics The Price System & The Micro Economy ( Oligopoly ) 17
Introduction to Game Theory Game theory studies strategic interaction (i.e. interdependency) between rational players in situations called games . There is strategic interaction between players if their individual payoff (i.e. reward) is not only determined by their own strategy but also by those of the other players . A game under normal (or strategic ) form is described by… …the set of players involved in the game. …the set of strategies that each player can implement. …the payoffs associated with every possible combination of strategies. Two-player finite games are usually represented by a payoff matrix .
Rock, Paper, Scissors R P S R (0 ; 0) (-10 ; 10) (10 ; -10) P (10 ; -10) (0 ; 0) (-10 ; 10) S (-10 ; 10) (10 ; -10) (0 ; 0) PLAYER 1 PLAYER 2
The Battle of the Sexes O F O (3 ; 2) (0 ; 0) F (0 ; 0) (2 ; 3) WOMAN MAN
The Prisoner’s Dilemma The prisoner’s dilemma is a game based on two premises : Each player has an incentive to choose a strategy that benefit itself at the other player’s expense . When both players act this way, both are worse off than if they had both acted cooperatively .
Prisoner’s Dilemma L C L (-3 ; -3) (-12 ; -1) C (-1 ; -12) (-10 ; -10) PLAYER 1 PLAYER 2
Best Response & Nash Equilibria A player’s best response is the strategy which yields the largest payoff , taking other players ’ strategies as given . A Nash Equilibrium (NE) is a strategy profile in which each player is best responding to the other players ’ strategies . In other words , a strategy profile is a NE if no player can be better off by unilaterally changing its strategy .
Rock, Paper, Scissors PLAYER 1 PLAYER 2 R P S R (0 ; 0) (-10 ; 10) (10 ; -10) P (10 ; -10) (0 ; 0) (-10 ; 10) S (-10 ; 10) (10 ; -10) (0 ; 0)
Rock, Paper, Scissors PLAYER 1 PLAYER 2 R P S R (0 ; 0) (-10 ; 10) (10 ; -10) P (10 ; -10) (0 ; 0) (-10 ; 10) S (-10 ; 10) (10 ; -10) (0 ; 0) This game does not have any NE.
Battle of the Sexes MAN O F O (3 ; 2) (0 ; 0) F (0 ; 0) (2 ; 3) WOMAN
Battle of the Sexes MAN O F O (3 ; 2) (0 ; 0) F (0 ; 0) (2 ; 3) WOMAN The strategy profiles (O ; O) and (F ; F) are both NE of this game.
Prisoner’s Dilemma PLAYER 1 L C L (-3 ; -3) (-12 ; -1) C (-1 ; -12) (-10 ; -10) PLAYER 2
Prisoner’s Dilemma PLAYER 1 L C L (-3 ; -3) (-12 ; -1) C (-1 ; -12) (-10 ; -10) PLAYER 2 The strategy profile (C ; C) is the unique NE of the game.
Practice Time! Compute the NE of the following game (if any ). PLAYER 1 PLAYER 2 D E F A (1 ; 13) (9 ; 10) (10 ; 5) B (8 ; 2) (6 ; 12) (4 ; 10) C (7 ; 14) (3 ; 4) (11 ; 15)
Practice Time! Compute the NE of the following game (if any ). PLAYER 1 PLAYER 2 D E F A (1 ; 13) (9 ; 10) (10 ; 5) B (8 ; 2) (6 ; 12) (4 ; 10) C (7 ; 14) (3 ; 4) (11 ; 15) The strategy profiled (C ; F) is the unique NE of the game.
Strategic Dominance For a given player , Strategy A strictly dominates Strategy B if Strategy A yields a strictly greater payoff than Strategy B, regardless of the strategies of the other players . A rational player will never play a strictly dominated strategy . For a given player , a strategy is said to be strictly dominant if it strictly dominates every other possible strategies . Therefore , a strictly dominant strategy is a best response to every strategies of the other players . If a strictly dominant strategy exists for every player , then the game has a strictly dominant strategy equilibrium .
Rock, Paper, Scissors PLAYER 1 PLAYER 2 R P S R (0 ; 0) (-10 ; 10) (10 ; -10) P (10 ; -10) (0 ; 0) (-10 ; 10) S (-10 ; 10) (10 ; -10) (0 ; 0)
Rock, Paper, Scissors PLAYER 1 PLAYER 2 R P S R (0 ; 0) (-10 ; 10) (10 ; -10) P (10 ; -10) (0 ; 0) (-10 ; 10) S (-10 ; 10) (10 ; -10) (0 ; 0) There are no strictly dominated strategies in that game.
Battle of the Sexes MAN O F O (3 ; 2) (0 ; 0) F (0 ; 0) (2 ; 3) WOMAN
Battle of the Sexes MAN O F O (3 ; 2) (0 ; 0) F (0 ; 0) (2 ; 3) WOMAN There are no strictly dominated strategies in that game.
Prisoner’s Dilemma PLAYER 1 L C L (-3 ; -3) (-12 ; -1) C (-1 ; -12) (-10 ; -10) PLAYER 2
Prisoner’s Dilemma PLAYER 1 L C L (-3 ; -3) (-12 ; -1) C (-1 ; -12) (-10 ; -10) PLAYER 2 For both players, Strategy C is a strictly dominant strategy. The strategy profile (C ; C) is a strictly dominant strategy equilibrium.
PLAYER 1 PLAYER 2 Task : Compute the strictly dominant strategy equilibrium of the following game (if any ). Practice Time! D E F A (1 ; 2) (-2 ; 2) (4 ; 4) B (4 ; 1) (1 ; 2) (6 ; 3) C (3 ; 4) (0 ; 2) (2 ; 6)
PLAYER 1 PLAYER 2 Task : Compute the strictly dominant strategy equilibrium of the following game (if any ). Practice Time! D E F A (1 ; 2) (-2 ; 2) (4 ; 4) B (4 ; 1) (1 ; 2) (6 ; 3) C (3 ; 4) (0 ; 2) (2 ; 6) For Player 1, Strategy B is strictly dominant. For Player 2, Strategy F is strictly dominant. The strategy profile (B ; F) is a strictly dominant strategy equilibrium.
Oligopoly An oligopoly is a market structure in which… …a few firms hold a large market share and face many buyers . …there are high barriers to entry , usually stemming from substantial IEoS . …firms are price-makers . …firms are interdependent (i.e. the profit made by each oligopolist is determined by the strategy profile of all firms in the industry). Nb : The number of sellers might not be relevant to define an oligopoly (i.e. a market in which there are many firms would still be considered an oligopoly if a few of them hold a sufficiently large market share). In an oligopoly, firms must observe the behaviour of their rivals and try to anticipate their reactions when choosing their own strategy .
Oligopoly In an oligopoly , the industry output can either be homogeneous or differentiated . Remark: An oligopoly consisting of only 2 firms is a duopoly . Each firm is known as a duopolist . Oligopolies can be modelled in many ways , depending on the nature of strategic interactions ( e.g . Bertand competition , Cournot competition , etc.). The difficulty in studying oligopoly is that the behaviour of firms (i.e. their market conduct ) can follow different routes. That is, there may be cut-throat competition between aggressive firms in some industries and cooperation between colluding firms in others.
Non-Price Competition In perfect competition , all firms sold the same product (i.e. firms could not differentiate their product in any way). It follows that perfectly competitive firms can only compete in price. In an oligopoly , however, firms may resort to non-price competition , a set of marketing strategies that allow firms to differentiate their product and gain a competitive advantage over their rivals . Firms will engage in non-price competition , in spite of the additional costs involved, because it is usually more profitable than selling for a lower price , and avoids the risk of a price war .
Pricing Strategies Limit pricing occurs when an incumbent firm sets a low enough price (i.e. the limit price) in order to deter new entrants from coming into the market . Predatory pricing occurs when a firm sets an extremely low price in order to force its competitors out of the market and exploit increased market power in the future . Remark : For both limit and predatory pricing , t he firm usually puts the price back up again once its objective has been achieved . A price war occurs where several firms in a market repeatedly lower their prices to outcompete their rivals and gain or defend market share . Typically, price wars occur in markets where non-price competition is weak or where firms find it difficult to collude .
Oligopoly & Collusion Within oligopolistic markets there is a constant tension within an individual firm as to whether to collude with its rivals (i.e. cooperative behaviour ) or compete with them (i.e. non- cooperative behaviour ). Collusion is an anti- competitive behaviour that takes place when rival firms enter into an agreement that restricts competition in order to increase their joint-profit . Nb : Collusion typically make consumers worse off because the price is likely to be higher than it would be if firms behaved non-cooperatively . It may, however, be beneficial if the extra profit gained by colluding firms is used to develop improved products or processes .
Oligopoly & Collusion H L H (4 ; 4) (0 ; 6) L (6 ; 0) (2 ; 2) FIRM A FIRM B
H L H ( 4 ; 4 ) (0 ; 6 ) L ( 6 ; 0) (2 ; 2) FIRM A FIRM B Oligopoly & Collusion Each firm has an incentive the deviate unilaterally from the cooperative equilibrium (i.e. to charge a low price rather than a high price)
H L H (4 ; 4) (0 ; 6) L (6 ; 0) (2 ; 2) FIRM A FIRM B Oligopoly & Collusion NON-COOPERATIVE EQUILIBRIUM For both firms, charging a low price is a strictly dominant strategy. The strategy profile (L ; L) is a strictly dominant strategy equilibrium. Nb : The strategy profile (L ; L) is also a NE.
Formal Collusion Formal collusion occurs when rival firms enter into a firmal agreement in order to limit competition and maximize their joint profit . Most formal collusive agreements result in lower output and higher price . Formal collusion can either be overt (i.e. open for everyone to see ) or covert (i.e. designed to be hidden from legal authorities). A group of firms engaging in formal collusion is known as a cartel . Most formal collusion is covert rather than overt , a notable exception being the Organization of the Petroleum Exporting Countries ( OPEC ).
Tacit Collusion Tacit (i.e. “ understood without being stated ”) collusion occurs when rival firms enter into an unwritten agreement (i.e. they do not actually communicate) aimed at restricting competition . Tacit collusion may be enforced through some form of price leadership (i.e. follow-the-leader informal agreement ), a situation in an oligopoly where one dominant firm sets or changes its price and others follow . An alternative is barometric price leadership which involves price leadership by a firm that has consistently been seen to judge market conditions accurately over time and is, therefore, seen as a good “barometer” of market trends . Also, firms might enforce an unwritten rule according to which they will not try to take away existing customers from other firms , or there may be an understanding that advertising expenditure should be kept low .
Collusion Stability By colluding , firms maximize their joint-profit but they might fail to maximize their individual profit . Therefore, firms within the collusive agreement - particularly those with lower costs - have an incentive to break ranks and increase their own output or sell at a lower price in order to increase their individual profit . Each member thus has an incentive to defect but there is risk of retaliation from other firms which might lead to a price war.
Collusion Stability Example : All OPEC members are aware that Saudi Arabia is in a position to flood the market with oil thereby significantly reducing its price which would penalise all members. If the incentives to cooperate are stronger than the incentives to defect , then collusion is said to be stable . Important remark: Joint-profit maximization is usually quite straightforward . However, the division rule of the obtained joint-profit is a very sensitive issue that can create tensions between the members (e.g. equal share for all members, share in proportion to the output produced, etc.).
Collusion Stability Collusion tends to be harder to form when … …there is a large number of firms (i.e. the larger the number of firms , the greater the possibility that at least one key participant will refuse to collude ). …the monitoring of price and output levels is difficult . …there are low barriers to entry (i.e. abnormal profits will attract new firms whose entry may jeopardize the stability of the collusive agreement ). ... firms have different cost structures (i.e. cost -efficient firms have low incentives to collude with less cost -efficient competitors ). … buyers have some degree of bargaining power which they can use to force suppliers to compete for their business and thus extract lower prices from them. …the industry is still immature (i.e. rapid changes in market conditions create an uncertainty that can make collusive agreements harder to create and sustain ).
Collusion & Law Collusion is illegal in most countries including EU countries and the USA. For this reason, firms wanting to create a cartel or collude in some other way have to collude secretly . Policies targeted at preventing oligopolistic industries from becoming or behaving like monopolies and breaking up existing ones are known as antitrust policies (e.g. Sherman Antitrust Act , 1890). In a trust , shareholders of all the major companies in an industry place their shares in the hands of a board of trustees who controls the company . This, in effect, merges the companies into a single firm that can engage in monopoly pricing .
In practice, competition authorities , such as the UK ’s Competition and Markets Authority, find it difficult and often inconclusive to investigate into anti-competitive behaviour and to prove either tacit or formal agreements . This is because price similarities can be simply due to similar cost structures rather than the outcome of a collusive agreement . In the 1990s , the U.S . instituted an amnesty program in which a cartel member received a much reduced penalty if it provided information on its co-conspirators . In addition, the U.S. Congress substantially increased maximum fines levied upon conviction . These two new policies were intended to make informing on cartel partners a dominant strategy . Collusion & Law
The Kinked Demand Curve Model The kinked demand curve model attempts to provide a non- cooperative rationale for the observed price stability in some oligopolistic markets . In particular , it shows that non- cooperative oligopolists may have no interest in moving away from a pre-established equilibrium . The kinked demand curve model assumes that oligopolists expect their rivals to react differently depending on the direction of the price change .
The Kinked Demand Curve Model If an oligopolist increases its price , then it expects that its rivals will maintain their initial price . Therefore , it expects to lose many consumers . In other words , it believes that its individual demand is price-elastic above the initial equilibrium price .
The Kinked Demand Curve Model If an oligopolist decreases its price , then it expects that its rivals will do likewise . Therefore , it expects to attract few consumers . In other words , it believes that its individual demand is price-inelastic below the initial equilibrium price .
The Kinked Demand Curve Model Therefore , the oligopolist expects that its individual demand curve to present a kink (i.e. a sudden change in slope ) at the initial equilibrium price . It follows that its MR curve has a jump discontinuity at the initial equilibrium level of output . For the initial point to form an equilibrium , it must be the case that the MC curve of the oligopolist goes through that jump discontinuity .
The Kinked Demand Curve Model Therefore , the oligopolist believes that it is neither optimal to increase nor to decrease its price . This model thus predicts periods of relative price stability where oligopolists may attempt to differentiate their product by engaging in non-price competition . Because the oligopolist does not move away from the initial equilibrium , it will be unable to ascertain whether its expectations were right. In other words , price stability is driven by the sole fear of rivals ’ potential reaction to changes in price .
The Kinked Demand Curve Model In classical economic theory , any change in MC or MR curve will be immediately reflected in a new equilibrium price or quantity . In the kinked demand curve model , however, the existence of a jump discontinuity in the MR curve implies that the MC can change without necessarily changing the equilibrium price or quantity . The resistance of price to change is known as price stickiness .
The Kinked Demand Curve Model The kinked demand curve model has some limitations : It is not supported by empirical evidence (i.e. prices in an oligopolistic market may be no more rigid than in other markets). It does not explain how the initial equilibrium forms . The model only deals with price competition and ignores the effects of non-price competition . The reason for price rigidity may have more to do with commercial practices than the firm’s awareness of the kinked demand curve .
Kinked Demand Curve AR 1 AR 2 MR 1 QUANTITY COST / REVENUE
Kinked Demand Curve AR 1 MR 2 AR 2 MR 1 QUANTITY COST / REVENUE
Kinked Demand Curve AR 1 MC 1 MR 2 AR 2 MR 1 QUANTITY COST / REVENUE
Kinked Demand Curve AR 1 MC 1 MR 2 AR 2 MR 1 QUANTITY COST / REVENUE THE OLIGOPOLIST INCREASES ITS PRICE SO IT SELLS 1 UNIT LESS . IT SAVES & IT GIVES UP SO THE PRICE INCREASE LEADS TO A FALL IN PROFIT .
Kinked Demand Curve AR 1 MC 1 MR 2 AR 2 MR 1 QUANTITY COST / REVENUE THE OLIGOPOLIST DECREASES ITS PRICE SO IT SELLS 1 ADDITIONAL UNIT . IT PAYS & IT EARNS SO THE PRICE DECREASE LEADS TO A FALL IN PROFIT .
Kinked Demand Curve AR 1 MC 1 MR 2 AR 2 MR 1 QUANTITY COST / REVENUE
Kinked Demand Curve AR 1 MC 1 MR 2 AR 2 MR 1 QUANTITY COST / REVENUE MC 2
Kinked Demand Curve AR 1 MC 1 MR 2 AR 2 MR 1 QUANTITY COST / REVENUE MC 2 MC 3