This paper presents a model of the European natural gas supply, GASMOD, which is structured as a two-stage-game of successive natural gas exports to Europe (upstream market) and wholesale trade within Europe (downstream market) and which explicitly includes infrastructure capacities. We compare three possible market scenarios: Cournot competition in both markets, perfect competition in both markets, and perfect competition in the downstream with Cournot competition in the upstream market (EU liberalization). We find that Cournot competition in both markets is the most accurate representation of today's European natural gas market, where suppliers at both stages generate a mark-up at the expense of the final customer (double marginalization). Our results yield a diversified supply portfolio with newly emerging (LNG) exporters gaining market shares. Enforcing competition in the European downstream market would lead to lower prices and higher quantities by avoiding the welfare-reducing effects of double marginalization. Binding infrastructure capacity restrictions strongly influence the results, and we identify bottlenecks mainly for intra-European trade relations whereas transport capacity in the upstream market is globally sufficient in the Cournot scenario.