ECOS 2201: Economics of Competition and Strategy Final Exam Synthesis Notes

Comprehensive vocabulary flashcards covering oligopoly theory, spatial differentiation, adverse selection, signaling models, bargaining theory, and auction theory from the ECOS 2201 lecture guide.

Cournot Best Response Function (Symmetric Firms)

The profit-maximizing individual output level given the aggregate output of rival firms $Q_{-i}$, defined as $q_i^*(Q_{-i}) = \frac{a - c - b Q_{-i}}{2b}$ .

Cournot Equilibrium Output per Firm

In an $n$-firm symmetric Cournot oligopoly with linear inverse demand $P(Q) = a - bQ$ and constant marginal cost $c$, the output produced by each firm is $q^* = \frac{a - c}{b(n + 1)}$.

Cournot Equilibrium Market Price

The prevailing market price in an $n$-firm symmetric Cournot equilibrium, given by $P^* = \frac{1}{n + 1} a + \frac{n}{n + 1} c = c + \frac{a - c}{n + 1}$.

Free Entry Zero-Profit Condition (Cournot with Fixed Cost)

The condition $\pi_i^*(n^*) = f$ where firms enter until individual operating profit equals fixed entry cost $f$, yielding an equilibrium number of active firms $n^* = \left\lfloor \frac{a - c}{\sqrt{b \cdot f}} - 1 \right\rfloor$.

Grim Trigger Strategy (Cournot Collusion)

A repeated-game punishment mechanism where any cheating from collusive output triggers an infinite reversion to the static Cournot-Nash equilibrium, sustaining collusion as a Subgame Perfect Equilibrium (SPE) iff $\delta \ge \frac{\pi_{\text{dev}} - \pi_{\text{collude}}}{\pi_{\text{dev}} - \pi_{\text{Cournot}}}$.

Bertrand Paradox

The result that simultaneous price competition between two identical firms with undifferentiated products and constant marginal cost $c$ drives prices down to marginal cost ($p_1^* = p_2^* = c$), yielding zero economic profit ($\pi_1^* = \pi_2^* = 0$).

Stackelberg Leadership Model

A sequential quantity-choice game where Firm 1 (leader) commits to output $q_1^* = \frac{a - c}{2b}$ by anticipating the follower's best response, leading the follower (Firm 2) to choose $q_2^* = \frac{a - c}{4b}$.

Indifferent Consumer Location ($\hat{x}$ in Hotelling Line)

The consumer location on $[0, 1]$ where net utility from purchasing at Firm 1 (at $0$) equals net utility from Firm 2 (at $1$), defined by $p_1 + t\hat{x} = p_2 + t(1 - \hat{x})$, yielding $\hat{x}(p_1, p_2) = \frac{p_2 - p_1 + t}{2t}$.

Maximal Differentiation Principle

In a two-stage Hotelling spatial game with quadratic transport costs $t(x - a)^2$ where locations are chosen before prices, firms choose opposite boundary endpoints ($a^* = 0$, $b^* = 1$) to soften subsequent price competition.

Minimal Differentiation Principle (Hotelling 1929)

When prices are fixed or regulated at $\bar{p}$, firms compete entirely for market share by clustering at the exact center of the market ($a^* = 1/2$, $b^* = 1/2$), matching the median voter theorem.

Spence-Mirrlees Condition (Single-Crossing Property)

The requirement that the marginal rate of substitution between total transfer $T$ and quality/quantity $q$ is strictly higher for high-type consumers than low-type consumers (high-type indifference curves are strictly steeper in $(q, T)$ space).

First-Best Benchmark (Full Information Price Discrimination)

The perfect price discrimination scenario where consumer types are directly observable, Individual Rationality binds with zero consumer surplus ($T_i^* = \theta_i v(q_i^*)$), and both types consume socially efficient quality levels satisfying $\theta_i v'(q_i^*) = C'(q_i^*)$.

Information Rent

The positive surplus $(\theta_H - \theta_L) v(q_L) > 0$ granted to the high-type consumer under asymmetric information to ensure incentive compatibility and prevent them from mimicking the low-type contract.

Second-Best Downward Quality Distortion

Under adverse selection, the optimal screening menu preserves efficiency for the highest type ($q_H^{SB} = q_H^{FB}$, 'no distortion at the top') but distorts the low type's quality downward ($q_L^{SB} < q_L^{FB}$) to reduce the high type's information rent.

Separating Equilibrium (Spence Education Model)

An equilibrium in which low types choose $e_L = 0$ and high types choose positive education $e^*$, supported across the continuum of education levels satisfying $\theta_L(w_H - w_L) \le e^* \le \theta_H(w_H - w_L)$.

Pooling Equilibrium (Spence Education Model)

An equilibrium where all workers choose an identical education level $e_P$ and receive the average pooled wage $\bar{w} = p w_H + (1 - p) w_L$, which exists when $e_P \le p \theta_L(w_H - w_L)$.

Cho-Kreps Intuitive Criterion

An equilibrium refinement that eliminates unreasonable off-path beliefs: if an off-path deviation could never be profitable for type $\theta_L$ even under the best possible wage $w_H$, employers must place probability zero on the deviator being type $\theta_L$.

The Riley Outcome

The unique separating equilibrium in the Spence signaling model surviving the Cho-Kreps Intuitive Criterion, where competition drives education to the minimum level necessary to deter mimicking: $e^* = \theta_L(w_H - w_L)$.

Nash Bargaining Product

The axiomatic solution selecting the allocation maximizing $\max_{(u_1, u_2) \in S} (u_1 - d_1)^\alpha (u_2 - d_2)^{1 - \alpha}$; under equal bargaining power ($\alpha = 1/2$) each player receives their disagreement point plus half the surplus: $u_i^* = d_i + \frac{1 - d_1 - d_2}{2}$.

Ultimatum Game Unique SPE

The finite-horizon subgame perfect equilibrium determined by backward induction where the responder accepts any non-negative payoff ($1 - x \ge 0$), allowing the proposer to offer $x^* = 1$ (or $1 - \varepsilon$) and capture the entire surplus.

Rubinstein Alternating Offers Model

An infinite-horizon bargaining game with discount factors $\delta_1$ and $\delta_2$, where Player 1 secures stationary equilibrium share $x_1^* = \frac{1 - \delta_2}{1 - \delta_1 \delta_2}$, simplifying to $x_1^* = \frac{1}{1 + \delta} > 1/2$ under symmetric patience.

Vickrey Auction (Second-Price Sealed-Bid)

A sealed-bid auction format where the highest bidder wins and pays the second-highest bid, making bidding one's true valuation ($b_i^* = v_i$) a weakly dominant strategy.

First-Price Sealed-Bid Auction (Symmetric BNE)

With $N$ risk-neutral bidders having valuations distributed uniformly on $[0, 1]$, the symmetric Bayesian Nash Equilibrium bidding strategy requires bid shading: $b^*(v_i) = \left(\frac{N - 1}{N}\right) v_i$.

The Winner's Curse

A phenomenon in common value auctions where the winning bidder is the one with the highest upward noise term; failing to condition on the fact that winning implies everyone else had a lower estimate results in systematic overbidding and losses.