Operations Research 2 Pt1 Skills Assessment

What is the main difference between linear and non-linear programming?

• The main difference is the color of the graphs used.

• The main difference is the number of variables involved.

• The main difference is the nature of the objective function and constraints.

• The main difference is the use of different mathematical symbols.

Explain the concept of Nash equilibrium in game theory.

• Nash equilibrium only applies to non-strategic games

• Each player's strategy is suboptimal given the strategies of the other players

• Each player's strategy is optimal given the strategies of the other players, and no player has an incentive to change their strategy unilaterally.

• Players have an incentive to change their strategy unilaterally

How is the objective function different in non-linear programming compared to linear programming?

• The objective function in non-linear programming is not necessarily a linear function.

• The objective function in non-linear programming has no constraints.

• The objective function in non-linear programming is always a linear function.

• The objective function in non-linear programming is not necessary for optimization.

Discuss the concept of dominant strategy in game theory.

• A dominant strategy is a strategy that is only the best choice for a player if they are the first to make a move.

• A dominant strategy is a strategy that is always the best choice for a player, regardless of the choices made by other players.

• A dominant strategy is a strategy that is only the best choice for a player if other players make certain choices.

• A dominant strategy is a strategy that is always the worst choice for a player, regardless of the choices made by other players.

What are the limitations of non-linear programming?

• Complexity, multiple local optima, specialized algorithms

• Simplicity, single global optimum, standard algorithms

• Unlimited solutions, easy optimization, general-purpose algorithms

• Straightforward, one solution, basic algorithms

Explain the concept of backward induction in game theory.

• Backward induction is a method used to solve finite extensive form games by working backwards from the end of the game to determine the optimal strategy for each player at each decision point.

• Backward induction is a method used to solve finite extensive form games by randomly selecting strategies for each player.

• Backward induction is a method used to solve finite extensive form games by determining the optimal strategy for each player at the beginning of the game.

• Backward induction is a method used to solve infinite extensive form games by working forwards from the beginning of the game.

Discuss the concept of Pareto efficiency in game theory.

• Pareto efficiency is a state where no player can be made better off without making another player worse off.

• Pareto efficiency is a state where all players are equally well off.

• Pareto efficiency is a state where one player dominates all others.

• Pareto efficiency is a state where all players are worse off compared to a previous state.

Explain the concept of mixed strategy in game theory.

• A mixed strategy is a strategy that is always the best choice for a player, regardless of the choices made by other players.

• A mixed strategy is a strategy that is only the best choice for a player if they are the first to make a move.

• A mixed strategy is a strategy that involves randomizing the choices made by a player based on certain probabilities.

• A mixed strategy is a strategy that is always the worst choice for a player, regardless of the choices made by other players.

What are the key characteristics of a non-linear programming problem?

• Dependence on the sequence of events

• Dependence on the current state and not on the sequence of events that preceded it

• Complexity, multiple local optima, specialized algorithms

• Dependence on the future state

What is the significance of the objective function in non-linear programming?

• The objective function in non-linear programming is always a quadratic function.

• The objective function in non-linear programming is not important for optimization.

• The objective function in non-linear programming is not necessarily a linear function.

• The objective function in non-linear programming is always a linear function.