Market Analysis Interactive

Game Theory

Strategic interaction between competitors. Understanding Nash equilibrium and best responses for pricing decisions in competitive markets.

🔒 The Prisoner's Dilemma

	Competitor Cooperates	Competitor Defects
You Cooperate	3, 3 Both win	0, 5 You lose
You Defect	5, 0 You win	1, 1 Nash Eq

In Pricing Terms

Cooperate: Keep hold rates reasonable
Defect: Slash hold to steal market share

Insight: Both firms are better off with moderate hold (3,3), but each has incentive to cut prices, leading to (1,1).

Pricing Decisions

2 10

📊 Best Response

Competitor's Hold 5%

Your Best Response 7.5%

Expected Profit 2.81

Market Outcome

You

Hold Rate 5%

Market Share 50%

Profit Score 2.50

Competitor

Hold Rate 5%

Market Share 50%

Profit Score 2.50

Matched pricing: Equal share, competing on other dimensions.

Common Game Structures

Prisoner's Dilemma

Both better off cooperating, but each has incentive to defect

Price wars: both cut prices, both lose margin

Defect-Defect (suboptimal)

Chicken

Worst outcome if both stay aggressive

Promotional spending: who backs down first?

One aggressive, one passive

Coordination

Both benefit from choosing same strategy

Market standards, feature matching

Multiple equilibria exist

♟️ Strategic Considerations

Competitive Dynamics

→ Monitor competitor pricing in real-time
→ Consider long-term reputation effects
→ Repeated games allow for cooperation
→ Differentiation can escape price wars

Signaling & Commitment

→ Price matching guarantees signal commitment
→ Public pricing = credible commitment
→ Promotional "shots across the bow"
→ Tit-for-tat builds cooperation

R Code Equivalent

# Game theory payoff analysis
calculate_payoff <- function(my_hold, their_hold) { 
  hold_diff <- their_hold - my_hold
  base_share <- 50
  share_gain <- hold_diff * 5  # 5% share per 1% hold diff
  my_share <- pmax(10, pmin(90, base_share + share_gain))
  profit <- my_share * my_hold / 100
  return(list(share = my_share, profit = profit))
}

# Find best response
best_response <- function(their_hold) { 
  holds <- seq(2, 10, by = 0.5)
  profits <- sapply(holds, function(h) calculate_payoff(h, their_hold)$profit)
  best_idx <- which.max(profits)
  return(list(hold = holds[best_idx], profit = profits[best_idx]))
}

# Nash equilibrium search
find_nash <- function() { 
  for (h1 in seq(2, 10, by = 0.5)) { 
    for (h2 in seq(2, 10, by = 0.5)) { 
      br1 <- best_response(h2)$hold
      br2 <- best_response(h1)$hold
      if (h1 == br1 && h2 == br2) return(c(h1, h2))
    }
  }
}

✅ Key Takeaways

• Nash equilibrium: no one benefits from changing
• Price wars often lead to lose-lose outcomes
• Best response depends on competitor actions

• Differentiation can escape price competition
• Repeated games allow cooperation to emerge
• Signaling and commitment matter