Reason Through an Interactive Trading Game

You are playing an interactive trading game with public information, private information available to you, and quotes from several bots. At each step, decide whether to trade, which quote to accept, whether to buy or sell, and how much to trade. New information is revealed as the game progresses. Explain your reasoning aloud. Keep track of your position and profit or loss, and update your valuation when the information changes. The exercise is about the decision process; no particular deck, payoff distribution, quote sequence, or numerical answer is supplied. ### Constraints & Assumptions - Establish what the traded claim pays at settlement and what information determines that payoff. - Do not assume that the bots are uninformed or that their quotes reveal no information. - Distinguish a current valuation from a realized cash flow and a final settlement payoff. - State any risk objective, position limit, fee, or short-selling rule you use. These rules must be clarified rather than guessed. ### Clarifying Questions to Ask - What is the settlement payoff, and how are public and private observations generated? - Can a bot's quote or willingness to trade carry information about the payoff? - Are there quantity limits, capital limits, fees, or restrictions on selling without an existing position? - Is performance judged by expected profit, realized profit, or a risk-adjusted objective? ### Part 1 — Value the Claim as Information Arrives Describe how you form an initial estimate and update it after a new observation. Explain which possibilities have become more or less likely and why the valuation changes, rather than simply announcing a new number. #### What This Part Should Cover - A clearly defined payoff and information set. - Conditional probabilities or conditional expectations appropriate to the available information. - A distinction between new evidence and information already included in the estimate. - Awareness that quotes and trades may contain additional evidence when counterparties are informed. ### Part 2 — Choose a Trade and Its Size Given the current estimates and available quotes, explain how you choose a counterparty, a direction, and a quantity. Describe how your existing position affects the next decision. #### What This Part Should Cover - Comparison of executable buy and sell prices with the relevant conditional value. - The option to decline a trade. - A size decision tied to limits, uncertainty, and existing exposure. - A distinction between the best displayed price and the best achievable trade after quantity limits or other costs. ### Part 3 — Track Profit and Evaluate Information Explain how you would maintain a running record of trades, cash, position, and profit or loss. Then describe how you would decide whether additional information is valuable before making a trade. #### What This Part Should Cover - Correct signs for purchases, sales, and long or short positions. - Separation of marked profit from final settled profit. - A way to compare decisions with and without a potential signal. - A retrospective explanation of whether a poor outcome came from an unreasonable decision or an unfavorable realization. ```hint After every action, separately update your beliefs and your transaction ledger. A valuation change can change marked profit without any new trade taking place. ``` ### What a Strong Answer Covers A strong response connects valuation, execution, exposure, and accounting in one consistent explanation. It states what is known before each decision, justifies a change in belief, and distinguishes an expected advantage from guaranteed profit. The review of the game should evaluate the reasoning available at the time rather than judging every choice only by the final outcome. ### Follow-up Questions - Could you rationally decline a positive-expected-value purchase after already building a large long position? - How could accepting a bot's quote change the appropriate estimate of the claim's value? - When can an informative signal have no value for your trading decision?