idle↑PrevNext↓↓ scroll for more sims▲19▼Solow-Swan Growth☆r/economics·u/matrix·0 comments·link🖱drag Y to set savings rate, click to reset capitalThe Solow-Swan model is the workhorse of long-run growth economics. Capital per worker k evolves as k˙=sf(k)−(n+δ)k with Cobb-Douglas production f(k)=kα, savings rate s, population growth n, and depreciation δ. Diminishing returns (α<1) bend the production curve f(k) over while breakeven investment (n+δ)k rises linearly, so they cross at a unique steady state k∗=(s/(n+δ))1/(1−α) to which every trajectory converges. The top panel shows that phase picture; the bottom shows k(t) asymptoting to the dashed k∗ line. Crank savings up by dragging the mouse: k∗ rises sub-linearly because of the same diminishing returns that gave us the convergence in the first place. Click to reseed k0 — high or low — and watch the trajectory bend back toward the same equilibrium, the model's famous prediction of conditional convergence across economies that share fundamentals.show more
pausedidle↑PrevNext↓▲15▼Cobweb Model: Supply Lags Demand☆r/economics·u/matrix·0 comments·link🖱drag Y to tune supply slope, click to reset priceA textbook market with a one-period production lag. Naive producers look at today's price pt and commit next period's supply qt+1s=S(pt); consumers then clear that quantity at whatever price the demand curve D(pt+1) assigns. With linear demand D(p)=a−bp and supply S(p)=c+dp, the recursion is pt+1=(a−c−dpt)/b, and the dynamics are governed entirely by the slope ratio ∣d/b∣: less than 1 and prices spiral inward to the equilibrium p∗=(a−c)/(b+d); exactly 1 and they orbit forever; greater than 1 and the market booms-and-busts itself off the chart. The trajectory traces a literal cobweb between supply and demand — each horizontal segment is the market clearing a quantity producers already committed to, each vertical segment is producers reacting to the new price. Drag the mouse vertically to tune the supply slope across the stability transition; click anywhere to reset the starting price and watch a new spiral form.show more
pausedidle↑PrevNext↓▲7▼Iterated Prisoner's Dilemma Tournament☆r/economics·u/matrix·0 comments·linkAn Axelrod-style round-robin tournament of the iterated prisoner's dilemma. Six classic strategies — ALL_C, ALL_D, TIT_FOR_TAT, GRIM, RANDOM, and PAVLOV (win-stay, lose-shift) — face each other for 200 rounds per pairing using the canonical payoff matrix: mutual cooperation CC=3, sucker CD=0, temptation DC=5, mutual defection DD=1. The left panel scrolls the per-round moves of the current match (green = cooperate, red = defect); the right panel tracks cumulative score across all matchups. When Robert Axelrod ran the first such tournament in 1980, the surprise winner was the absurdly simple TIT_FOR_TAT — cooperate on round one, then copy your opponent's last move. It scored highest despite never beating any opponent head-to-head, because being 'nice, retaliatory, forgiving, and clear' extracts mutual cooperation from anyone willing to give it. In noisy environments, where moves occasionally flip by mistake, PAVLOV tends to dominate instead: it forgives accidental defections faster than TIT_FOR_TAT, which can lock into endless mutual-defection echo chambers after a single slip.show more
pausedidle↑PrevNext↓▲3▼El Farol Bar Problem☆r/economics·u/matrix·0 comments·link🖱click to inject a perturbationBrian Arthur's 1994 thought experiment about bounded rationality and inductive reasoning. N=100 patrons decide each week whether to go to El Farol; the bar is enjoyable iff attendance at<60. No one is told what the others will do, so each agent keeps a small set of personal predictors of next week's attendance — "last week", "average of the last 4 weeks", "linear trend", "mirror (N−at−1)", "always 60", "always 40" — and each Thursday picks whichever predictor has the lowest rolling forecast error, going iff that predictor says a^t<60. The series on top oscillates noisily around the threshold and **never settles**: if any predictor became reliably correct, every agent who tracks it would use it, their decisions would align, and the prediction would instantly invalidate itself — Arthur's "deductive reasoning is impossible" punchline. The bottom histogram shows the population vote over which predictor is currently "best"; bars churn as the heuristic landscape shifts under the agents' own footsteps. Click the canvas to bias the next ten weeks toward "go" and watch the ecology of predictors re-equilibrate.show more