Matrix solved, threat tested: in this MT445 Unit 8 game theory analysis the ferry's fare-war warning fails backward induction, while a binding $17 contract deters entry. Searches like "mt 445 unit 8 assignment example", "mt445 unit 8 sample" and "mt445 unit 8 example" land here.
What a finished MT445 Unit 8 game theory analysis looks like
Seven pages built around a three-by-three matrix and a small game tree. The matrix gives weekly contribution in thousands of dollars for day-tripper fares of $20, $24 and $28 at the ferry against $17, $21 and $25 at the catamaran, computed from a stated pair of demand equations. At $20 the ferry earns 73.0 against the catamaran's $17, 80.5 against its $21 and 88.1 against its $25. Best responses are marked cell by cell: $20 is dominant for the ferry, and the catamaran's best reply to $20 is $17, so the only pure-strategy equilibrium sits at 73.0 and 26.2. The tree adds entry. Against a $560,000 entry cost over a 24-week season, accommodation leaves the entrant $68,992 ahead, while a $16 fare war would leave it $47,744 behind.
How a MT445 Unit 8 example is structured
Assumptions are stated before any cell is filled: fares set simultaneously each season, a demand pair both operators know, and marginal costs of $2.90 a rider for the ferry and $4.40 for the faster, thirstier catamaran. The matrix is solved by best response rather than by inspection, with the dominance argument shown so the equilibrium can be checked. A short section notes the dilemma inside it: at $24 and $21 both would earn more, yet neither fare survives the other's temptation to undercut. The entry tree carries the credibility argument. Working backward, once the catamaran is in, a war pays the ferry about $5,400 a week less than accommodating, so the threat collapses. Commitment comes next: a season contract with island hotels at $17, signed before entry, removes the ferry's softer option, and the paper prices what happens if deterrence fails anyway.
Assumptions before payoffs
Simultaneous fare-setting each season, known demand, and marginal costs of $2.90 and $4.40 a rider are stated first. Every payoff in the matrix can be recomputed from them.
Nine cells, best responses marked
A $20 fare beats $24 and $28 for the ferry in every column, and the catamaran answers $20 with $17. The single pure-strategy equilibrium pays 73.0 and 26.2 thousand dollars a week.
A better cell neither can hold
At $24 and $21 the ferry would earn 78.3 and the catamaran 30.5, both higher. Each would undercut from there, the paper shows, and an agreement to stay put is no recommendation to make.
Backward through the entry tree
After entry, fighting at $16 pays the ferry 67.6 thousand a week against 73.0 for accommodating. A rational ferry would not carry out the threat, so the catamaran enters and clears $68,992 a season.
A contract that makes $17 binding
Season packages with island hotels at $17 leave the entrant about $19,904 short, so it stays out, and the ferry earns roughly $360,000 more a season. Should the catamaran enter regardless, the ferry loses about $90,864.
Where marks go in MT445 Unit 8
Game theory papers in MT445 are frequently marked down for finding an equilibrium and stopping, when the unit's second question, which threats are believable, carries much of the weight. Graders tend to expect backward induction shown on the tree, not asserted. Equilibria claimed without best responses marked, or a dominant strategy announced without checking every column, cannot be verified. Payoffs invented cell by cell, with no demand model behind them, make the matrix look arbitrary. Mistaking the cooperative cell for the equilibrium is a classic slip, and so is advising the rivals to settle on higher fares, which raises collusion concerns no paper should wave past. Commitment arguments earn credit only when the commitment is binding and costed; praising deterrence without pricing the case where the entrant comes anyway skips the risk.
Get a MT445 Unit 8 example written to your instructions
Paste in the payoff matrix or competitive scenario from your Unit 8 prompt, with the rubric and any assumptions your section fixes, such as simultaneous or sequential moves. Within 24-48h a sample arrives with best responses marked, equilibria found and checked, and every threat tested for credibility. No fee is charged for a first custom sample.
MT445 Unit 8 questions, answered
How do I find the Nash equilibrium in a payoff matrix?
Mark each player's best response. For every column, underline the row player's highest payoff; for every row, underline the column player's highest. Any cell where both payoffs are underlined is a pure-strategy Nash equilibrium. Check for a dominant strategy first, since it shortens the search, and say whether the game has one equilibrium, several or none in pure strategies.
What makes a threat credible?
A threat is credible if carrying it out would serve the threatener when the moment arrives. Solve the game backward: if, after the rival acts, the punishing move pays less than the alternative, a rational player will not follow through, and the rival can ignore the threat. Commitments that remove the alternative, such as binding contracts, can restore credibility.
Can the analysis recommend that competitors coordinate prices?
No. Explicit agreements between competitors to fix prices are illegal under US antitrust law, and a paper recommending one will lose credit whatever its game theory. You can explain why the cooperative outcome is unstable, and you can discuss lawful strategic moves, such as commitments, capacity choices or differentiation, that change the payoffs.