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Tariffs and imperfect international           competition               Game Theory            By Eranga Kavirathna       ...
   Two Stage Game       Dynamic game with lots of players and imperfect        information.   Imperfect information    ...
   There are more players in this Game.   Each country has a          1. government,          2. a firm, and          3....
   Two governments, 1 and 2, simultaneously    choose their tariff rates, denoted by t1, t2.   Firm 1 from country 1 and...
   After observing the tariff rates chosen by the two    countries, firm 1 and 2 simultaneously chooses    quantities for...
How high of a tariff should eachgovernment impose?It depend on,   Firms behavior (Profit maximization)   Objective of go...
Tariffs and imperfect internationalcompetition Firm 1s play for its profit: Firm 2s play for its profit:                  ...
Tariffs and imperfect internationalcompetition Country 1s Gov. play for its total welfare: sum of the consumers surplus en...
Backward induction:subgame between the two firms   Here we will find the Nash equilibrium of the subgame between   the two...
Backward induction: whole gameBoth countries know that two firms best response for any pairCountry 1 maximizes (          ...
Backward induction:subgame between the two firms  Here we will find the Nash equilibrium of the subgame between the  two f...
Tariffs and imperfect internationalcompetitionThe subgame-perfect Nash equilibriumThe subgame-perfect outcome             ...
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Tariffs and-imperfect-international-competition

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Tariffs and-imperfect-international-competition

  1. 1. Tariffs and imperfect international competition Game Theory By Eranga Kavirathna 1
  2. 2.  Two Stage Game  Dynamic game with lots of players and imperfect information. Imperfect information  A player may not know exactly Who has made What choices when he has an opportunity to make a choice. 2
  3. 3.  There are more players in this Game. Each country has a 1. government, 2. a firm, and 3. consumers for a firm’s output. (consumers are treated as passive in this game) So there are 4 players, 1. Two governments 2. Two firms The players change in the second stage of the game. 3
  4. 4.  Two governments, 1 and 2, simultaneously choose their tariff rates, denoted by t1, t2. Firm 1 from country 1 and firm 2 from country 2 produce a homogeneous product for both home consumption and export. 4
  5. 5.  After observing the tariff rates chosen by the two countries, firm 1 and 2 simultaneously chooses quantities for home consumption and for export, denoted by (h1, e1) and (h2, e2), respectively. Market price in two countries Pi(Qi)=a–Qi, for i=1, 2. Q1=h1+e2, Q2=h2+e1. Both firms have a constant marginal cost c. Each firm pays tariff on export to the other country. 5
  6. 6. How high of a tariff should eachgovernment impose?It depend on, Firms behavior (Profit maximization) Objective of government policy (Total welfare, Maximize TAX revenue, Maximize Home firm revenue or Max. Consumer Surplus) 6
  7. 7. Tariffs and imperfect internationalcompetition Firm 1s play for its profit: Firm 2s play for its profit: 7
  8. 8. Tariffs and imperfect internationalcompetition Country 1s Gov. play for its total welfare: sum of the consumers surplus enjoyed by the consumers of country 1, firm 1s profit and the tariff revenue where . Country 2s Gov. play for its total welfare: sum of the consumers surplus enjoyed by the consumers of country 2, firm 2s profit and the tariff revenue where . 8
  9. 9. Backward induction:subgame between the two firms Here we will find the Nash equilibrium of the subgame between the two firms for any given pair of . Firm 1 maximizes (first derivation) FOC: Firm 2 maximizes (first derivation) FOC: 9
  10. 10. Backward induction: whole gameBoth countries know that two firms best response for any pairCountry 1 maximizes ( )Plugging what we got into country 1s objective functionFOC:By symmetry, we also get 10
  11. 11. Backward induction:subgame between the two firms Here we will find the Nash equilibrium of the subgame between the two firms for any given pair of . Given , a Nash equilibrium of the subgame should satisfy these equations. Solving these equations gives us 11
  12. 12. Tariffs and imperfect internationalcompetitionThe subgame-perfect Nash equilibriumThe subgame-perfect outcome 12

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