Managerial Economics

DOT96a Managerial Economics By Leonard Treuren Bachelor of TEW & ERB – Second Year

2024 – 2025

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Lecture 1: Game theory and competition

Game Theory: Fundamentals

= mathematical tool used to represent strategic interactions in a treatable way “Games” → stylized representation of agents’ goals, information and capabilities

• Predict outcomes (players with conflicting goals)
• Understand factors that gives some players an advantage
• Identify problems that hinder good outcomes (and avoid them)

Real life:

Decision-makers have goals/preferences about outcomes of their interactions Preferences like revenues, market value give a certain payoff

In a game:

Preferences can be ranked (have a numerical value = payroll) → high numerical value = outcome more preferred

Strategies = actions that agents can chose to achieve their goals

- Action: setting different prices, time you study for a course

- Strategy: studying a lot/ almost nothing for a course

Outcome of a game = result of all player’s strategies

Agents (players) are individually rational:

• They have rational preferences (over the outcomes)

Preference between options, liking one more than the other (all else equal)

• They are payoff-maximizing (=/= selfish)

Goal in the long run: maximizing profits → “you want to get things that you like more” e.g. if you have a love for charity, when maximalizing you don’t get the money

or for some companies is maximalizing the goals: largen the consumer basis

• Not always about the making “the most” money

3 main categories of games:

➢ Strategic games ➢ Extensive games ➢ Sequential and Bayesian games 2 / 4

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Strategic games

• Static: one-shot (1 interaction) and simultaneous choice (players choose strategy without knowing

the strategy of the others)

o In reality: price setting – companies are looking at each other

• Complete or perfect information: all players know the actions/ consequences (not the decision of

other players)

Complete information ≠ certainty:

Games involve measurable risk → risk under uncertainty (e.g. you don’t know the exact price of stock tomorrow) Asymmetric information (some players know things others don’t) → auction off building of a bridge to different companies

e.g. best out of 5

→ One company enters a market; the other waits to see the outcome of the other one before entering himself

Strategic games: abstract form

- Set of players: P = {Player1, Player2}

- Set of actions: AP1 = {Defect, Cooperate}, AP2 = {Defect, Cooperate}

• Players’ payoff functions

Normal (payoff-matrix) form

• Rows = the row-player’s actions
• Columns = the column-player’s actions
• Each cel = action profile → within always the payoff

(preference for an outcome, action profiles = cause)

Complete/Perfect information Asymmetric information Static Strategic games Rock – Paper – Scissors Bayesian games Sealed-Bid Auction Dynamic Extensive games, repeated games Chess, Monopoly

Sequential (Bayesian) games Poker

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Finding an equilibrium:

Elimination of dominated strategies

P2: X → P1: D

P2: Y → P1: D

P2: T → P1: C

• There is not one strategy that is always the best
• Regardless of what P2 does: if P1 plays D you will always have a better outcome than if you play H
• D strictly dominates H
• A rational player would never play H → We eliminate action H

P1: D → P2: X

P1: C → P2: X

• X strictly dominates (eliminate Y &T)
• P2 has a strategy that will always give you the best outcome

(one’s H is eliminated)

P2: X → P1: D

(D, X) = equilibrium in dominant strategies

• Only possible outcome, very predictable
• Too restrictive (most games don’t have one)

More general equilibrium: Nash Equilibrium

= an action profile such that each player’s strategy maximizes that player’s payoff conditional on the other players’ strategies.

• No players can benefit by unilaterally deviating (changing their decision alone)
• NE has a resting point and has nothing optimal about it
• When several players move at the same time → often better off
• Each player is playing their best response to the other players’ strategies (doing what’s optimal)

• In a NE, each player achieves the highest possible payoff
• An equilibrium in dominant strategies is also always a NE
• Players can never choose a strictly dominated strategy in a NE
• In a NE, the sum of players’ payoffs is higher than in any other combination of strategies
• A strategic game with 2 players always has at least one NE in pure strategies
• If a NE exists, then it is unique

False True True False (vb. 1) False (vb.2) False (vb. 3)

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