We propose that the mathematical representation of situations of strategic interactions, i.e., of games, should separate the description of the rules of the game from the description of players’ personal traits. Yet, we note that the standard extensive-form partitional representation of information in sequential games does not comply with this separation principle. We offer an alternative representation that extends to all (finite) sequential games the approach adopted in the theory of repeated games with imperfect monitoring, that is, we describe the flow of information accruing to players rather than the stock of information retained by players, as encoded in information partitions. Mnemonic abilities can be represented independently of games. Assuming that players have perfect memory, our flow representation gives rise to information partitions satisfying perfect recall. Different combinations of rules about information flows and of players mnemonic abilities may give rise to the same information partition . All extensive-form representations with information partitions, including those featuring absentmindedness, can be generated by some such combinations.
Macroeconomic outcomes depend on the distribution of markups across firms and over time, making firm-level markup estimates key for macroeconomic analysis. Methods to obtain these estimates require data on the prices that firms charge. Firm-level data with wide coverage, however, primarily comes from financial statements, which lack information on prices. We use an analytical framework to show that trends in markups or the dispersion of markups across firms can still be well-measured with such data. Finding the average level of the markup does require pricing data, and we propose a consistent estimator for such settings. We validate the analytical results with simulations of a quantitative macroeconomic model and firm-level administrative production and pricing data. Our analysis supports the use of financial data to measure trends in aggregate markups.