UGC NET - Game Theory — non-cooperative games. Online Test (MCQ Quiz)

1. What is the fundamental assumption of a non-cooperative game?

A) Players can make binding agreements. B) Players act independently to maximize their own payoffs. C) Players share information perfectly. D) Players collude to achieve a common goal.

2. In game theory, what does a 'strategy' represent for a player?

A) A single action taken by the player. B) A complete plan of action for every possible situation. C) The payoff the player receives. D) The set of all possible moves in the game.

3. A situation in a non-cooperative game where no player can improve their payoff by unilaterally changing their strategy is called:

A) A dominant strategy equilibrium. B) A Pareto efficient outcome. C) A Nash equilibrium. D) A cooperative outcome.

4. What characterizes a 'dominant strategy' in a non-cooperative game?

A) It yields the best payoff regardless of the other players' strategies. B) It is the strategy chosen by the majority of players. C) It is the strategy that leads to the highest possible payoff for the player. D) It is a strategy that is only optimal when other players play a specific move.

5. If a game has a dominant strategy equilibrium, it implies that:

A) All players have a unique best response to every possible strategy of the other players. B) Players will necessarily achieve the best possible collective outcome. C) Cooperation is inevitable. D) The game has multiple Nash equilibria.

6. The Prisoner's Dilemma is a classic example of a non-cooperative game. In this game, the dominant strategy for both players is typically:

A) Cooperate B) Defect C) Remain Silent D) Confess

7. In the Prisoner's Dilemma, the Nash equilibrium results in:

A) Both players cooperating and receiving a moderate sentence. B) One player cooperating and the other defecting, leading to a lighter sentence for the defector. C) Both players defecting and receiving a harsher sentence than if they had cooperated. D) Both players remaining silent and receiving the lightest possible sentence.

8. What is a 'mixed strategy' in game theory?

A) A strategy that involves a combination of pure strategies with certain probabilities. B) A strategy that is always the best response. C) A strategy where a player chooses only one action. D) A strategy that leads to a cooperative outcome.

9. A Nash equilibrium in mixed strategies exists when:

A) Each player's mixed strategy is a best response to the other players' mixed strategies. B) All players choose the same mixed strategy. C) The expected payoffs for all pure strategies are equal. D) The sum of probabilities in the mixed strategy is less than one.

10. Which theorem guarantees the existence of at least one Nash equilibrium (possibly in mixed strategies) for any finite non-cooperative game?

A) The Coase Theorem B) The Core Theorem C) The Minimax Theorem D) Nash's Existence Theorem

11. In a zero-sum game, what is the relationship between the payoffs of the players?

A) The sum of the payoffs is always zero. B) One player's gain is another player's equal loss. C) Both players can achieve positive payoffs simultaneously. D) The payoffs are independent of each other.

12. The Minimax Theorem, by John von Neumann, applies to:

A) All non-cooperative games. B) Cooperative games only. C) Finite zero-sum games. D) Games with more than two players.

13. What is the 'maximin' strategy in a zero-sum game?

A) Maximizing the minimum possible payoff. B) Minimizing the maximum possible loss. C) Maximizing the maximum possible payoff. D) Minimizing the minimum possible loss.

14. What is the 'minimax' strategy in a zero-sum game?

A) Minimizing the maximum possible loss. B) Maximizing the minimum possible payoff. C) Minimizing the minimum possible payoff. D) Maximizing the maximum possible payoff.

15. In a two-player zero-sum game, if a saddle point exists, it corresponds to:

A) A Nash equilibrium in pure strategies. B) A cooperative outcome. C) A situation where both players can improve their payoffs. D) A mixed strategy equilibrium.

16. A 'saddle point' in a payoff matrix of a zero-sum game is an entry that is:

A) The minimum of its row and the maximum of its column. B) The maximum of its row and the minimum of its column. C) The minimum of its row and the minimum of its column. D) The maximum of its row and the maximum of its column.

17. Which of the following is NOT a characteristic of non-cooperative games?

A) Binding agreements are possible. B) Players act in their self-interest. C) Strategies are pre-committed. D) Payoffs are determined by the combination of strategies chosen.

18. What does the concept of 'subgame perfection' apply to in non-cooperative game theory?

A) Games with a finite number of players and strategies. B) Sequential games. C) Simultaneous move games. D) Zero-sum games only.

19. A strategy profile is subgame perfect if it represents a Nash equilibrium in:

A) Every subgame of the original game. B) The overall game only. C) A specific type of cooperative game. D) The first move of the game only.

20. The concept of backward induction is used to find subgame perfect Nash equilibria in:

A) Finite horizon sequential games. B) Simultaneous move games. C) Infinite horizon games. D) Games with imperfect information.

21. Consider a sequential game. Backward induction starts by determining the optimal strategy at:

A) The last decision nodes. B) The first decision node. C) The middle decision nodes. D) All decision nodes simultaneously.

22. In a game of incomplete information, what does a player not know?

A) The actions of other players. B) The payoffs of other players. C) Their own payoffs. D) The rules of the game.

23. Bayesian Nash Equilibrium is a solution concept for games with:

A) Incomplete information. B) Perfect information. C) Sequential moves. D) Zero sum payoffs.

24. What is an 'information set' in a game of imperfect information?

A) A collection of nodes where a player cannot distinguish which node they are at. B) A set of all possible strategies. C) A node where a player makes a decision. D) The payoff received by a player.

25. In a game of imperfect information, a player's strategy must specify an action for:

A) Every information set they might face. B) Only the first information set. C) The information set they are currently in. D) A single predetermined action.

26. What is the primary difference between cooperative and non-cooperative game theory?

A) In cooperative games, binding agreements are possible; in non-cooperative games, they are not. B) Non-cooperative games always have a unique solution. C) Cooperative games focus on individual rationality, while non-cooperative games focus on group rationality. D) Non-cooperative games involve simultaneous moves, while cooperative games involve sequential moves.

27. Which of the following best describes the concept of 'correlated equilibrium'?

A) A situation where players' strategies are correlated through an external mediator or signal. B) A situation where players' strategies are independent. C) A situation where players form binding agreements. D) A situation where players always play their dominant strategy.

28. The concept of 'repeated games' extends non-cooperative game theory by:

A) Allowing the same game to be played multiple times. B) Introducing cooperative elements. C) Reducing the number of players. D) Eliminating the possibility of mixed strategies.

29. In an infinitely repeated Prisoner's Dilemma, cooperation can be sustained as a Nash equilibrium if:

A) Players are sufficiently patient (discount factor is high). B) Players are not patient (discount factor is low). C) The game is played only once. D) Players always defect.

30. The 'Folk Theorem' in repeated games suggests that:

A) Any feasible and individually rational payoff profile can be sustained as a Nash equilibrium in an infinitely repeated game. B) Only the stage game's Nash equilibrium can be sustained. C) Cooperation is never possible in repeated games. D) The discount factor does not affect the equilibrium outcomes.

31. What is a 'pure strategy' in game theory?

A) A strategy where a player chooses a single action with certainty. B) A strategy that involves randomization. C) A strategy that is always optimal. D) A strategy that leads to a cooperative outcome.

32. A game is considered to have 'perfect information' if:

A) At every decision point, the player knows the complete history of the game. B) All players know each other's payoffs. C) All players move simultaneously. D) Players can form binding agreements.

33. Which of the following is a key assumption for applying the concept of Nash equilibrium?

A) Players are rational and seek to maximize their own payoffs. B) Players cooperate to achieve a common goal. C) Players have perfect information about each other's strategies. D) Players can make binding agreements.

34. What does the term 'payoff matrix' represent in a non-cooperative game?

A) A table showing the payoffs for each player for every possible combination of strategies. B) A graphical representation of player strategies. C) The set of all possible moves in the game. D) The probability distribution of outcomes.

35. In a simultaneous move game, players choose their strategies:

A) Without knowing the strategy chosen by the other player. B) After observing the other player's move. C) In sequence. D) Through negotiation.

36. The concept of 'rationalizability' is a refinement of Nash equilibrium that eliminates:

A) Strategies that are not best responses to any belief about opponents' strategies. B) Strategies that are not dominant. C) Mixed strategies. D) Subgame imperfect strategies.

37. A strategy profile is 'iteratively strictly dominated' if it can be eliminated by:

A) Repeatedly removing strictly dominated strategies. B) Finding a Nash equilibrium. C) Applying backward induction. D) Assuming players have perfect information.

38. What is the 'extensive form' of a game?

A) A representation of the game as a decision tree, showing sequences of moves and information sets. B) A table showing payoffs for all strategy combinations. C) A graphical representation of payoffs. D) A description of player preferences.

39. The 'normal form' of a game is equivalent to:

A) The strategic form or payoff matrix. B) The extensive form. C) A sequential game representation. D) A game with perfect information.

40. In a game with imperfect information, players must form beliefs about:

A) Which information set they are in. B) The total number of strategies available. C) The opponent's payoffs. D) The probability of the game ending.

41. What is the 'discount factor' (delta) in the context of repeated games?

A) A measure of how much players value future payoffs relative to current payoffs. B) The probability of the game ending. C) The number of times the game is repeated. D) The payoff received in the first round.

42. A 'Pareto improvement' is a change to a different outcome where:

A) At least one player is better off, and no player is worse off. B) All players are better off. C) One player is better off, and another is worse off. D) The sum of payoffs increases.

43. A 'Pareto efficient' outcome is one where:

A) No Pareto improvement is possible. B) All players receive the same payoff. C) The sum of payoffs is maximized. D) Every player has a dominant strategy.

44. In non-cooperative game theory, the focus is on:

A) Individual players' optimal strategies given the strategies of others. B) The collective welfare of all players. C) The possibility of binding agreements. D) The efficiency of outcomes.

45. Which of the following is a common application of non-cooperative game theory?

A) Oligopoly pricing decisions. B) Public goods provision in large groups. C) International treaty negotiations. D) Formation of coalitions.

46. A 'threat' in a sequential game is credible if:

A) It is in the best interest of the player making the threat to carry it out if the condition arises. B) It is simply stated by a player. C) It is never carried out. D) It leads to a cooperative outcome.

47. Subgame perfection eliminates Nash equilibria that rely on:

A) Non-credible threats. B) Credible threats. C) Dominant strategies. D) Mixed strategies.

48. What is the main challenge in analyzing games with a large number of players?

A) The combinatorial explosion of strategy profiles and the difficulty of finding equilibria. B) The lack of dominant strategies. C) The impossibility of mixed strategies. D) The absence of Nash equilibria.

49. Which solution concept is most appropriate for analyzing a situation where players might not fully trust each other's rationality?

A) Rationalizability. B) Nash Equilibrium. C) Subgame Perfection. D) Bayesian Nash Equilibrium.

Game Theory — non-cooperative games. - Online Test

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